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lara [203]
2 years ago
13

Find the value of x.

Mathematics
2 answers:
Lisa [10]2 years ago
8 0

{x}^{2}  +  {(x  + 3)}^{2}  =   {( \sqrt{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
Cerrena [4.2K]2 years ago
3 0
x^2 + (x + 3)^2 = (\sqrt{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
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