A 45-45-90 triangle has a hypotenuse of length 14 units. What is the length of one of the legs?

1 Answer
Nov 14, 2015

One side length is equal to #sqrt(98)#.


We can start off by establishing that this triangle is a right, isosceles triangle. We can say this because of the converse of the isosceles triangle theorem, which states if two angles are congruent, then then 2 sides are congruent.

What we can conclude from the previous statement, is that the two legs are equal length. Therefore, we can use a modified version of the Pythagorean Theorem. That is, since #a ~= b#, we can substitute #a# in for #b#. That makes our equation #a^2 + a^2 = c^2#.

We know that the hypotenuse is #14#, so we can plug that into the equation. #a^2 + a^2 = 14^2 => 2a^2 = 196#. We can divide each side by 2, and square root each side to rid of the exponent.

That leaves us with #a = sqrt(98).#