Scroll:Whole Numbers >> Other Heuristics >> ps (1263)

Written Instructions:

For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..

For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.

Leave your answers in the simplest form or correct to two decimal places.


 

1)  

The figure is formed by 2 squares. The side of each square is a whole number. If the total area of the figure is 100 cm2, what is the perimeter of the figure



cm


Answer:_______________




2)  

The figure shows a square which is cut off from a bigger square. The corresponding sides of both squares are whole numbers. If the areas of the two squares are 100 cm2, find the perimeter of the figure (inside and outside).

cm


Answer:_______________




3)  

The figure is formed by 2 squares. The side of each square is a whole number. If the total area of the figure is 13 cm2, what is the perimeter of the figure



cm


Answer:_______________




4)  

The figure is formed by 3 squares. The side of each square is a whole number. If the total area of the figure is 195 cm2, find the perimeter of the figure.

cm


Answer:_______________




5)  

The figure shows a square which is cut off from a bigger square. The corresponding sides of both squares are whole numbers. If the areas of the two squares are 74 cm2, find the perimeter of the figure (inside and outside).

cm


Answer:_______________




6)  

The figure is formed by 2 squares. The side of each square is a whole number. If the total area of the figure is 53 cm2, what is the perimeter of the figure



cm


Answer:_______________




7)  

The figure is formed by 3 squares. The side of each square is a whole number. If the total area of the figure is 90 cm2, find the perimeter of the figure.

cm


Answer:_______________




8)  

The figure is formed by 2 squares. The side of each square is a whole number. If the total area of the figure is 97 cm2, what is the perimeter of the figure



cm


Answer:_______________




9)  

The figure shows a square which is cut off from a bigger square. The corresponding sides of both squares are whole numbers. If the areas of the two squares are 146 cm2, find the perimeter of the figure (inside and outside).

cm


Answer:_______________




10)  

The figure is formed by 3 squares. The side of each square is a whole number. If the total area of the figure is 125 cm2, find the perimeter of the figure.

cm


Answer:_______________




 

1)  

The figure is formed by 2 squares. The side of each square is a whole number. If the total area of the figure is 100 cm2, what is the perimeter of the figure



Answer: 44 cm


SOLUTION 1 :

Step 1:

List of whole numbers:

1     2     3     4     5     6     7     8     9     10     11

List of corresponding square values:

1    4    9     16    25    36   49   64   81    100   121

Since the total area of the figure is formed by two squares, you look for two square values whose sum is equal to 100 cm2.

From the list of square values, notice that, 36 + 64 = 100 cm2

Therefore, the area of the small square is 36 cm2 and the area of the big square is 64 cm2.

Their corresponding sides are 6 cm and 8 cm respectively.

Step 2:

8 + 8 + 8 + 2 + 6 + 6 + 6 = 44 cm

The perimeter of the figure is 44 cm.



2)  

The figure shows a square which is cut off from a bigger square. The corresponding sides of both squares are whole numbers. If the areas of the two squares are 100 cm2, find the perimeter of the figure (inside and outside).

Answer: 56 cm


SOLUTION 1 :

Step 1:


List of whole numbers:


1     2     3     4     5     6     7     8     9     10     11


List of corresponding square values:


1    4    9     16    25    36   49   64   81    100   121


Since the total area of the figure is formed by two squares, you look for two square values whose sum is equal to 100 cm2.


From the list of square values, notice that, 36 + 64 = 100 cm2


Therefore, the area of the small square is 36 cm2 and the area of the big square is 64 cm2.


Their corresponding sides are 6 cm and 8 cm respectively.


Step 2:


6 + 6 + 6 + 6 + 8 + 8 + 8 + 8 = 56 cm


The perimeter of the figure is 56 cm.



3)  

The figure is formed by 2 squares. The side of each square is a whole number. If the total area of the figure is 13 cm2, what is the perimeter of the figure



Answer: 20 cm


SOLUTION 1 :

Step 1:


List of whole numbers:


1     2     3     4     5     6     7     8     9     10     11


List of corresponding square values:


1    4    9     16    25    36   49   64   81    100   121


Since the total area of the figure is formed by two squares, you look for two square values whose sum is equal to 13 cm2.


From the list of square values, notice that, 9 + 4 = 13 cm2


Therefore, the area of the small square is 4 cm2 and the area of the big square is 9 cm2.


Their corresponding sides are 2 cm and 3 cm respectively.


Step 2:


4 + 4 + 4 + 2 + 2 + 2 + 2 = 20 cm


The perimeter of the figure is 20 cm.



4)  

The figure is formed by 3 squares. The side of each square is a whole number. If the total area of the figure is 195 cm2, find the perimeter of the figure.

Answer: 68 cm


SOLUTION 1 :

Step 1:


List of whole numbers:


1     2     3     4     5     6     7     8     9     10     11


List of corresponding square values:


1    4    9     16    25    36   49   64   81    100   121


Since the total area of the figure is formed by three squares, you look for three square values whose sum is equal to 195 cm2.


From the list of square values, notice that, 25 + 49 + 121 = 195 cm2


Therefore, the area of the small square is 25 cm2, the area of the medium square is 49 cm2  and the area of the big square is 121cm2.


Their corresponding sides are 5 cm, 7 cm and 11 cm respectively.


Step 2:


5 + 5 + 5 + 7 + 7 + 7 + 11 + 11 + 4 + 6 = 68 cm


The perimeter of the figure is 68 cm.



5)  

The figure shows a square which is cut off from a bigger square. The corresponding sides of both squares are whole numbers. If the areas of the two squares are 74 cm2, find the perimeter of the figure (inside and outside).

Answer: cm


SOLUTION 1 :

Step 1:


List of whole numbers:


1     2     3     4     5     6     7     8     9     10     11


List of corresponding square values:


1    4    9     16    25    36   49   64   81    100   121


Since the total area of the figure is formed by two squares, you look for two square values whose sum is equal to 74 cm2.


From the list of square values, notice that, 25 + 49 = 74 cm2


Therefore, the area of the small square is 25 cm2 and the area of the big square is 49 cm2.


Their corresponding sides are 5 cm and 7 cm respectively.


Step 2:


5 + 5 + 5 + 5 + 7 + 7 + 7 + 7 = 48 cm


The perimeter of the figure is 48 cm.



6)  

The figure is formed by 2 squares. The side of each square is a whole number. If the total area of the figure is 53 cm2, what is the perimeter of the figure



Answer: 32 cm


SOLUTION 1 :

Step 1:

List of whole numbers:

1     2     3     4     5     6     7     8     9     10     11

List of corresponding square values:

1    4    9     16    25    36   49   64   81    100   121

Since the total area of the figure is formed by two squares, you look for two square values whose sum is equal to 53 cm2.

From the list of square values, notice that, 4 + 49 = 53 cm2

Therefore, the area of the small square is 4 cm2 and the area of the big square is 49 cm2.

Their corresponding sides are 2 cm and 7 cm respectively.

Step 2:

7 + 7 + 7 + 5 + 2 + 2 + 2 = 32 cm

The perimeter of the figure is 32 cm.



7)  

The figure is formed by 3 squares. The side of each square is a whole number. If the total area of the figure is 90 cm2, find the perimeter of the figure.

Answer: 46 cm


SOLUTION 1 :

Step 1:


List of whole numbers:


1     2     3     4     5     6     7     8     9     10     11


List of corresponding square values:


1    4    9     16    25    36   49   64   81    100   121


Since the total area of the figure is formed by three squares, you look for three square values whose sum is equal to 90 cm2.


From the list of square values, notice that, 16 + 25 + 49 = 58 cm2


Therefore, the area of the small square is 16 cm2, the area of the medium square is 25 cm2 and the area of the big square is 49 cm2.


Their corresponding sides are 4 cm, 5 cm and 7 cm respectively.


Step 2:


4 + 4 + 4 + 7 + 7 + 5+ 5 + 5 + 2 + 3 = 46 cm


The perimeter of the figure is 46 cm.



8)  

The figure is formed by 2 squares. The side of each square is a whole number. If the total area of the figure is 97 cm2, what is the perimeter of the figure



Answer: 44 cm


SOLUTION 1 :

Step 1:


List of whole numbers:


1     2     3     4     5     6     7     8     9     10     11


List of corresponding square values:


1    4    9     16    25    36   49   64   81    100   121


Since the total area of the figure is formed by two squares, you look for two square values whose sum is equal to 97 cm2.


From the list of square values, notice that, 16 + 81 = 97 cm2


Therefore, the area of the small square is 16 cm2 and the area of the big square is 81 cm2.


Their corresponding sides are 4 cm and 9 cm respectively.


Step 2:


9 + 9 + 9 + 5 + 4 + 4 + 4 = 44 cm


The perimeter of the figure is 44 cm.



9)  

The figure shows a square which is cut off from a bigger square. The corresponding sides of both squares are whole numbers. If the areas of the two squares are 146 cm2, find the perimeter of the figure (inside and outside).

Answer: 64 cm


SOLUTION 1 :

Step 1:

List of whole numbers:

1     2     3     4     5     6     7     8     9     10     11

List of corresponding square values:

1    4    9     16    25    36   49   64   81    100   121

Since the total area of the figure is formed by two squares, you look for two square values whose sum is equal to 146 cm2.

From the list of square values, notice that, 25 + 121 = 146 cm2

Therefore, the area of the small square is 25 cm2 and the area of the big square is 121 cm2.

Their corresponding sides are 5 cm and 11 cm respectively.

Step 2:

5 + 5 + 5 + 5 + 11 + 11 + 11 + 11 = 64 cm

The perimeter of the figure is 64 cm.



10)  

The figure is formed by 3 squares. The side of each square is a whole number. If the total area of the figure is 125 cm2, find the perimeter of the figure.

Answer: 54 cm


SOLUTION 1 :

Step 1:


List of whole numbers:


1     2     3     4     5     6     7     8     9     10     11


List of corresponding square values:


1    4    9     16    25    36   49   64   81    100   121


Since the total area of the figure is formed by three squares, you look for three square values whose sum is equal to 125 cm2.


From the list of square values, notice that, 25 + 36 + 64 = 125 cm2


Therefore, the area of the small square is 25 cm2, the area of the medium square is 36 cm2  and the area of the big square is 64cm2.


Their corresponding sides are 5 cm, 6 cm and 8 cm respectively.


Step 2:


5 + 5 + 5 + 6 + 6 + 6 + 8 + 8 + 3 + 2 = 54 cm


The perimeter of the figure is 54 cm.