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.
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=40⇒a1=10
Similarly, perimeter of second square =4a2
Given, perimeter of second square = 96
According to the question,
4a2=96⇒a2=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+a22⇒a2=(10)2+(24)2=100+576=676⇒a=√676=26 m
[taking square root on both sides]
Perimeter of another square
=4a
=4×26
=104 m