Question

the perimeters of two squares are 40m and 96m respectively.find the perimeters of another square equal in are to the sum of first two squares

Answer 1

$\mathbb{ SOLUTION }$ :

Let the side of two squares be 'a' and 'b'.

Then,

The perimeter of the first square = 4a

Given,
perimeter of first square = 40

According to the question,
=> 4a = 40
=> a = 40÷4
=> a = 10

Similarly,
perimeter of second square = 4b

Given,
perimeter of second square = 96

According to the question,
=> 4b = 96
=> b = 96÷4
=> b = 24

Let, x be the side of another square.

Then,
area of another square = x²

$\therefore$ Area of another square = sum of the areas of first and second squares

= (a)² + (b)²

=> x² = (10)² + (24)²

=> x² = 100 + 576

=> x² = 676

=> x = $\sqrt{676}$

=> x = 26


Perimeter of another square = 4x = 4*26 = 104m

So,
the perimeter of another square is 104m.

Answer 2

Hey !!

 Let us consider the side of two squares x and y

Therefore

Perimeter(1st square) = 4x

Perimeter(1st square) = 40 m

            = 4x = 40

            = x = 40 ÷ 4

            = x = 10 m

Now,

The Perimeter(2nd square) = 4 y

The Perimeter(2nd square) = 96

= 4 y = 96

= y = 96 ÷ 4

= y = 24

Therefore, Let us consider z should be the side of Another square

Area of 2nd square be (z)²

= x² + y²

= z² = (10)²+(24)²

= z² = 100 + 576

= z² = √676

= z = 26

The Perimeter of other square  = 4z = 4(26)  

        = 104 m

HOPE IT HELPS YOU !!