Question

Find the value of x.

Answer 1

`{x}^(2) + {(x + 3)}^(2) = {( √(117) )}^(2) \\ 2 {x}^(2) + 6x + 9 = 117 \\ 2 {x}^(2) + 6x - 108 = 0\\ {x }^(2) + 3x - 54 = 0 \\ (x + 9)(x - 6) = 0 \\ x = - 9 \: or \: 6 \\ but \: x > 0 \\ so \: the \: answer \: is \: x = 6`
hope this would help you

Answer 2

`x^2 + (x + 3)^2 = (√(117))^2`


`x^2 + x^2 + 6x + 9 = 117`


`2x^2 + 6x -108 = 0`


`x^2 + 3x - 54 = 0`


`(x + 9)(x - 6) = 0`


`x + 9 = 0 ~~or~~ x - 6 = 0`


`x = -9 ~~ or~~ x = 6`

Since the side of a triangle cannot have a negative length, we discard the solution x = -9.

Answer: x = 6