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Question

Question 140

The perimeters of two squares are 40 m and 96 m, respectively. Find the perimeter of another square equal in area to the sum of the first two squares.


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Solution

Let the side of two squares be a1 and a2.
Then, perimeter of first square =4a1
Given, perimeter of first square = 40
According to the question,
4a1=40a1=10
Similarly, perimeter of second square =4a2
Given, perimeter of second square = 96

According to the question,
4a2=96a2=24

Let a be the side of another square.
Then, area of another square =a2
Area of another square = Sum of the areas of first and second squares
= Area of first square + Area of second square
=a21+a22a2=(10)2+(24)2=100+576=676a=676=26 m
[taking square root on both sides]

Perimeter of another square
=4a
=4×26
=104 m


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