# A right angle triangle has sides of x+6, x+5 and x-2, how do you write the expression for the perimeter?

Apr 23, 2016

, $p = 3 x + 9 = 30$

#### Explanation:

Being rt angled

${\left(x + 6\right)}^{2} = {\left(x + 5\right)}^{2} + {\left(x - 2\right)}^{2}$
$\implies \cancel{{x}^{2}} + 12 x + 36 = \cancel{{x}^{2}} + 10 x + 25 + {x}^{2} - 4 x + 4$
$\implies {x}^{2} - 6 x - 7 = 0$
$\implies {x}^{2} - 7 x + x - 7 = 0$
$\implies \left(x - 7\right) \left(x + 1\right)$
$\therefore x = 7$
perimeter, $p = x + 6 + x + 5 + x - 2$
, $p = 3 \times 7 + 9 = 30$