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).

Explanation:

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).