# 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 #16 # and the triangle has an area of #40 #. What are the lengths of sides A and B?

##### 2 Answers

#### Explanation:

Small letters for triangle sides please, dearies.

My favorite formula for the area of a triangle

Let

Check:

The altitude

Lengths of sides A and B

#### Explanation:

Isosceles Triangle means two sides are equal.

The area of triangle is

Area =

The given are base and the area.

first determine the height before finding A and B.

Substitute Area = 40 and Base C = 16

to the formula

Area =

or

or

divide both side by

to get the

since you have the height

cut into two congruent lengths by the height, since we are dealing with an Isosceles triangle, the entire base measures 16, half of the base measures 8.

Now we have two Right Triangles

using Pythagorean Theorem

64 + 25 =

89 =

89 is a prime number