Question

(v) Around a square pool, there is a footpath of
width 2 m. If the area of the footpath is 5/4 times
that of the pool, find the area of the pool.​

Answer 1

Answer:

Let the side of the square pool be x .

5/4 × Area of square pool = Area of footpath

5/4 × Area of square pool = Total area - Area of pool

5/4 × Area of square pool + Area of pool = Total area

(5/4 + 1)(Area of pool) = (x + 4)^2

(9/4)(x)^2 = x^2 + 8x + 16

9x^2 = 4( x^2 + 8x + 16 )

9x^2 = 4x^2 + 32x + 64

5x^2 - 32x - 64 = 0

5x^2 - 40x + 8x - 64 = 0

5x (x - 8) + 8(x - 8) = 0

(5x + 8)(x - 8) = 0

5x + 8 = 0 or x - 8 = 0

x = -8/5

x = 8

Here x = -8/5 is rejected

Therefore , x = 8

Area of pool = 8×8 = 64 m^2

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