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Question

# The perimeters of two squares are 68 cm and 60 cm.Find the perimeter of the third square whose area is equal to the difference of the area of these two squares .

## The correct answer is: ∴ Perimeter of the third square is 32 cm.

### Perimeter of a square = 4 × side

Area of a square = side^{2}

Step-by-step solution:-

A. For Square 1-

Perimeter = 68 cm

∴ 4 × side = 68

∴ side = 68 / 4

∴ side = 17 cm

Area = side^{2}

∴ Area = 17^{2}

∴ Area = 289 cm^{2} .................................................... (Equation i)

B. For Square 2-

Perimeter = 60 cm

∴ 4 × side = 60

∴ side = 60 / 4

∴ side = 15 cm

Area = side^{2}

∴ Area = 15^{2}

∴ Area = 225 cm^{2} .................................................... (Equation ii)

C. For Square 3-

Area = Difference of Areas of Square 1 & 2

∴ Area = Area of Square 1 - Area of Square 2

∴ Area = 289 - 225 .................................................. (From Equations i & ii)

∴ Area = 64

∴ Side^{2} = 64 ............................................................. (Area of a square = side^{2})

∴ Side = 8 .................... (Taking square root both the sides) ............................ (Equation iii)

Perimeter = 4 × side

∴ Perimeter = 4 × 8 ............................................................................................ (From Equation iii)

Final Answer:-

∴ Perimeter of the third square is 32 cm.

∴ Perimeter = 32 cm.

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