Question

Around a square pool , there is a footpath is 7/9 times that of pool , find the area of the pool

Answer 1

let the side of the square pool be xm
the side of the square pqrs = ( x +2+2 )m
= (x +4)m
area of the footpath = 5/4 × area of the pool
area of square pqrs x - area of square pool = 5/4 area of the square pool
(x+4)² - x² = 5/4 ( x)
x² + 8 x + 16 - x² = 5/4 x²
8x + 16 = 5/4 x²
4(8x+16)=5x²
32x +64 = 5x²
5x²- 40x + 8x - 64 = 0
5x(x-8)+8(x-8)=0
(5x+8) (x-8)=0
5x+8=0. or x-8=0
5x= -8. or. x=8
x=-8/5. or. x=8

x = -8/5 not possible
so , x = 8
so, the area of the pool = x ²
= 8²
= 64m²