An isosceles triangle has sides A, B, and C, such that sides A and B have the same length. Side C has a length of #7 # and the triangle has an area of #112 #. What are the lengths of sides A and B?

1 Answer
Mar 2, 2018

Side A and Side B both are #32.76.#

Explanation:

Given Information
#area = 112#
#Side C = 7#
#Side A and Side B = ?#

The area equation of a triangle is #Area = 1/2(base)(height)#
We know the area, and the base (side C), so we solve for height.

#112 = 1/2(7)(height)#
#112 = 3.5height#
#height = 32#

Now that we know the height, we can use the Pythagorean theorem to solve the side lengths.

#a^2 + b^2 = c^2# Recall theorem
#(7)^2 + (32)^2 = c^2# Solving for c
#49 + 1024 = c^2#
#c = sqrt1073#
#c = 32.76#

Since side A and side B are the same length, then #32.76# is the side length for both.