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?

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Answer 1 · 2018-03-02T23:44:31

Side A and Side B both are $32.76.$

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.

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 7 and the triangle has an area of 112 112 . What are the lengths of sides A and B?