Question

around a square coil there is a Footpath of feet to metre if the area of Footpath is 5 by 4 times that of the pool find the area of the book

Answer 1

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

This is the right question.

Answer:-Let one side of the square pool be 'x' m.So, the side of the footpath is (x+2+2) m, which is equal to (x+4) m.

So, area of the pool=side²
=x² m²

Area of the outer square=side²
=(x+4) m²
=(x²+4²+2×x×4) [ (a+b)²=a²+b²+2ab ]
=(x²+16+8x) m²

We know that the area of the footpath=Area of the outer square-Area of the pool

It is also given that,the footpath is 5/4 times that of pool.

ATQ:-

5/4×x²=(x²+16+8x)-x²

5/4×x²=x²+16+8x-x²

5/4×x²=x²-x²+16+8x

5/4×x²=16+8x

5x²=4(16+8x)

5x²=64+32x

5x²-64-32x=0

5x²-32x-64x=0 (Rearrange the terms and do middle term factorisation)

5x²+8x-40x-64=0

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

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

So, 1) x-8=0

x=8

2) 5x+8=0

5x=-8

x=-8/5

Here, we have to take the positive value out of the two solutions, that is the first one, because area can never be negative.

So, the area of the pool=x² m²
=8² m²
=64 m²

Answer 2

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