Question

The square pool was turned into a rectangular one and it's area was enlarged by a factor of 5 by enlarging one side of the pool by 3 meters and the other side by 14. What are the new dimensions of the pool?​

Answer 1

$\boxed{ \tt{the \: dimensions \: are : }}\\ \boxed{ \tt{b = 9 \: meters} }\\ \boxed{ \tt{l = 20 \: meters}}$

$5 {s}^{2} = (3 + s) \times (14 + s) \\ 5 {s}^{2} = {s}^{2} + 17s + 42 \\ {4s}^{2} - 17s - 42 = 0 \\ s = \frac{ - ( - 17) + \sqrt{ {( - 17)}^{2} - 4(4)(42)} }{2(4)} \\ s = \frac{17 + 31}{8} \\ s = 6 \\ hence \to \:the \: dimensions \: are : \\ b = s + 3 = 6 + 3 = 9 \: meters \\ l = s + 14 = 6 + 14 = 20 \: meters$