# How do you find the lengths of the sides of a right triangle given the legs x and x+1 and the hypotenuse 7?

Jul 1, 2016

Legs of the triangle are 4.424 and 5.524

#### Explanation:

Write an equation using Pythagoras' Theorem.

${x}^{2} + {\left(x + 1\right)}^{2} = {7}^{2}$
${x}^{2} + {x}^{2} + 2 x + 1 - 49 = 0$

2x^2 +2x -48 = 0 " " ÷2

${x}^{2} + x - 24 = 0$

Solve by Completing the square method:

${x}^{2} + x + {\left(\frac{1}{2}\right)}^{2} = 24 + {\left(\frac{1}{2}\right)}^{2}$
${\left(x + \frac{1}{2}\right)}^{2} = 24 + \frac{1}{4}$

$x + \frac{1}{2} = \pm \sqrt{\frac{97}{4}}$
$x = \frac{+ \sqrt{97}}{2} - \frac{1}{2} \text{ or } x = \frac{- \sqrt{97}}{2} - \frac{1}{2}$

$x = 4.424 \text{ or } x = - 5.424$ (reject as a side)

Legs of the triangle are 4.424 and 5.524