# How do you use the Pythagoras Theorem to find side length of triangle abc if ac=7 and bc=3?

Jul 1, 2016

"Side length" of triangle is $6.324$

#### Explanation:

As the "side length" is to be found using Pythagoras theorem, it is apparent that of known sides $a c = 7$ and $b c = 3$, $a c$ the greater one is the hypotenuse and we have to find $a b$.

Now according to Pythagoras theorem square of hypotenuse is equal to sum of the squares of other two sides, hence

${7}^{2} = {3}^{2} + {\left(b c\right)}^{2}$ or

$49 = 9 + {\left(b c\right)}^{2}$

or ${\left(b c\right)}^{2} = 49 - 9 = 40$

Hence $b c = \sqrt{40} = \sqrt{2 \times 2 \times 10} = 2 \sqrt{10} = 2 \times 3.162 = 6.324$