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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.

Solution:

Given, the perimeters of two squares are 40 and 96 metres.

Another square is equal in area to the sum of the first two squares.

We have to find the perimeter of another square.

We know that perimeter of square = 4(side)

Considering square 1,

Given, perimeter = 40 m

40 = 4(side)

Side of square 1 = 40/4

= 10 m

Considering square 2,

Given perimeter = 96 m

96 = 4(side)

Side of square 2 = 96/4

= 24 m

We know area of square = (side)²

Area of square 1 = (10)² = 100 m²

Area of square 2 = (24)² = 576 m²

Sum of area of two squares = 100 + 576

= 676 m²

According to the question,

Area of another square = 676 m²

(side)² = 676

Taking square root,

Side of another square = 26 m

Now, perimeter of another square = 4(26)

= 104 m

Therefore, the required perimeter is 104 m.

✦ Try This: The perimeters of two squares are 20 and 24 metres respectively. Find the perimeter of another square equal in area to the sum of the first two squares.

☛ Also Check: NCERT Solutions for Class 8 Maths

NCERT Exemplar Class 8 Maths Chapter 3 Problem 140

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

Summary:

The perimeters of two squares are 40 and 96 metres respectively. The perimeter of another square is equal in area to the sum of the first two squares, is 104 m.

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