Question

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?

Answer 1

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.