In a right angled triangle, the hypotenus is (3x + 2) cm long. If the other two sides are (x + 3) cm and 3x cm how do you find x?

Jun 1, 2018

$x = 1 \text{ or } x = 5$

Explanation:

$\text{since they are right angled triangles we can use}$
$\textcolor{b l u e}{\text{Pythagoras' theorem}}$

$\text{the square on the hyotenuse "="sum of squares on the}$
$\textcolor{w h i t e}{\times \times \times \times \times \times \times \times \times \times \times} \text{other 2 sides}$

${\left(3 x + 2\right)}^{2} = {\left(x + 3\right)}^{2} + {\left(3 x\right)}^{2}$

$\cancel{9 {x}^{2}} + 12 x + 4 = {x}^{2} + 6 x + 9 \cancel{+ 9 {x}^{2}}$

$\text{subtract "12x+4" from both sides}$

$0 = {x}^{2} - 6 x + 5$

$0 = \left(x - 1\right) \left(x - 5\right)$

$x - 1 = 0 \Rightarrow x = 1$

$x - 5 = 0 \Rightarrow x = 5$

$\text{substitute these values into the given sides}$

$\text{to obtain "3,4,5 " or } 8 , 15 , 17$

$\text{both well known "color(blue)"Pythagorean triples}$