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Jlenok [28]
3 years ago
5

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?​
Mathematics
1 answer:
ozzi3 years ago
7 0

\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

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