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.

Answer 1

Let the side of two squares be $a_1$ and $a_2$.
Then, perimeter of first square $=4a_1$
Given, perimeter of first square = 40
According to the question,
$4a_1=40\Rightarrow a_1=10$
Similarly, perimeter of second square $=4a_2$
Given, perimeter of second square = 96

According to the question,
$4a_2=96\Rightarrow a_2=24$

Let $a$ be the side of another square.
Then, area of another square $=a^2$
$\therefore$ Area of another square = Sum of the areas of first and second squares
= Area of first square + Area of second square
$=a_1^2+a_2^2\Rightarrow a^2=(10{)}^2+(24{)}^2=100+576=676\Rightarrow a=\sqrt{676}=26m$
[taking square root on both sides]

Perimeter of another square
$=4a$
$=4\times 26$
$=104m$