Question

This is from pre calc

Answer 1

The dimensions are 106, 47,116

Explanation:

`when \: {(x + 10)}^(2) = {y }^(2) + {x}^(2) \\ then \: {y}^(2) = {(x + 10)}^(2) - {x}^(2) \\ {y}^(2) = {x}^(2) + 20x + 100 - {x}^(2) \\ {y}^(2) = 20x + 100 \\ then \: y = √(20x + 100) \\ when \\ area \: of \:rectangular \: = x * y \\ then \\ x * √(20x + 100) = 5000 \\ Square \: both \: sides \\ {x}^(2) (20x + 100) = 25000000 \\ 20 {x}^(3) + 100 {x}^(2) - 25000000 = 0 \\ Using \: the \: analysis \\ x = 106 \: \: \: or \: x = - 55.5 \\ \: We \: reject \: the \: negative \: solution \: because \: there \: is \: no \: length \: in \: the \: negative \\ then \: the \: dimensions \: are \: \\ 106 \\ 47 \\ 116`