# How do you find the missing side of a right triangle given a = 5, b = 10?

Apr 10, 2016

Use of Pythagora'sTheorem

#### Explanation:

$h y {p}^{2}$ =$o p {p}^{2}$ + $a {\mathrm{dj}}^{2}$
Replace values....

${10}^{2}$ = ${5}^{2}$ + $s i {\mathrm{de}}^{2}$
100= 25 + $s i {\mathrm{de}}^{2}$
100-25= $s i {\mathrm{de}}^{2}$
75= $s i {\mathrm{de}}^{2}$
side= $\sqrt{75}$

Apr 10, 2016

$5 \sqrt{5}$

#### Explanation:

Note: I am considering $a \mathmr{and} b$ are the right containing sides

Consider the diagram

Use Pythagoras theorem

color(blue)(a^2+b^2=c^2

Where,

$a \mathmr{and} b$ are the right-containing sides, and $c$ is the Hypotenuse

(Hypotenuse is the longest side of a right triangle)

$\rightarrow {5}^{2} + {10}^{2} = {c}^{2}$

$\rightarrow 25 + 100 = {c}^{2}$

$\rightarrow 125 = {c}^{2}$

Take the square root of both sides

$\rightarrow \sqrt{125} = {\sqrt{c}}^{2}$

color(green)(rArrc=sqrt125=sqrt(5*5*5)=5sqrt5