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
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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
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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
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