# Given that the hypotenuse of a right-angled triangle is 41cm, and the sum of the sides of the triangle is 49cm, How do you find the lengths of the other two sides?

Nov 9, 2015

9 and 40

#### Explanation:

Let $x$ be the length of 1 of the missing sides
=>$49 - x$ is the length of the other missing side

By pythagorean theorem, we have

${x}^{2} + {\left(49 - x\right)}^{2} = {41}^{2}$

${x}^{2} + 2401 - 98 x + {x}^{2} = 1681$

$2 {x}^{2} - 98 x + 2401 - 1681 = 0$

$2 {x}^{2} - 98 x + 720 = 0$

${x}^{2} - 49 x + 360 = 0$

$\left(x - 9\right) \left(x - 40\right) = 0$

$\implies x = 9 , x = 40$

If we select any of the two values of $x$ and compute for the other side given $49 - x$, we will get the unselected value