Question

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

Answer 1

Answer:

Step-by-step explanation:

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

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 =

=> x = 26

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

So,

the perimeter of another square is 104m.

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