Question

solve quadratic equation

Answer 1

Let the side of square pool be x
Then side of plot including footpath is x+4
Then area of pool is x² and area of footpath is (x+4)²-x²

Given,
${(x + 4)}^{2} - {x}^{2} = \frac{5}{4} {x}^{2} \\ 8x + 16 = \frac{5}{4} {x}^{2} \\ 5 {x}^{2} - 32x - 64 = 0 \\ x = \frac{32 + \: \: or \: \: - \sqrt{ {( - 32)}^{2} - 4 \times 5 \times - 64} }{2 \times 5} \\ x = \frac{32 + \: or \: - 48}{10} \\ taking \: \: positive \: \: value \: for \: \: x \\ x = \frac{32 + 48}{10} = 8$
Thus area of pool = 8² = 64 m²