Question

The perimeters of two squares are 40 cm and 32 cm. Find the perimeter of
a third square whose area is equal to the difference of the areas of the two
squares.
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Answer 1

Given:

• Perimeter of two squares are 40 cm and 32 cm.
• Area of third sqaure is equal to difference between areas of the two squares.

To find:-

• Perimeter of third sqaure.

SolutioN:-

• First we need areas of both square beacuse it is given that area of third sqaure is equal to difference between areas of two squares.
• Then, We need side for area of both squares.So,

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We know that,

✤ Perimeter of square = 4 × side ✤

For first square,

Perimeter of first square = 40 cm.

⇒4 × side = 40

⇒side = 40/4

⇒side = 10 cm

Side of first sqaure is 10 cm.

For second sqaure

Perimeter of second sqaure = 32 cm.

⇒4 × side = 32

⇒side = 32/4

⇒side = 8 cm

Side of second sqaure is 8 cm.

• We need area of two squares for area of third sqaure.So,

We know that,

✤ Area of square = side × side✤

For first sqaure

• Side = 10 cm

⇒10 × 10

⇒100 cm²

Area of First square is 100 cm².

For second square

• Side = 8 cm

⇒8 × 8

⇒64 cm²

Area of second square is 64 cm²

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Then,

Area of third square = Area of first square - Area of second square

⇒100 - 64

⇒36 cm²

Area of second square = 36 cm²

We need side of third square for perimeter.

So,

Side × side = Area of third square

↦Side² = 36

↦Side = √36

↦Side = 6

Side of third square = 6 cm.

Perimeter of third square = 4 × side

⇒4 × 6

⇒24

Therefore, Perimeter of third square is 24 cm.