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The perimeters of two squares are 48 cm and 40 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares.


1. 8√ 11 cm
2. 4√ 11 cm
3. √ 11 cm
4. 22 cm

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Correct Answer - Option 1 : 8√ 11 cm

Given

The perimeters of two squares are 48 cm and 40 cm

Area of third square is equal to difference of area of the two square

Formula used

Perimeter of square = 4 × side

Area of square = (side)2

Calculation

Let side of square 1 = x

Perimeter of square 1 = 48 cm

⇒ 4x = 48

⇒ x = 12cm

⇒ Area = (12)2

⇒ 144 cm2

Side of square 2 = y

⇒ 4y = 40

⇒ y = 10 cm

⇒ Area = (10)2

⇒ 100 cm2

Area of third square = area of square 1 and 2

⇒ Area = 144 - 100

⇒ 44 cm2

Side of third square = √ 44

⇒ Perimeter = 4a

⇒ 4√ 44 cm

⇒ 8√ 11 cm

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