Question

The pennant below is in the shape of an isosceles triangle. Determine and state the length of the base.

A. 24
B. 5
C. 10
D. 12

Answer 1

C. 10

Explanation:

we know that

The height of an isosceles triangle divide the triangle into two equal right triangles.

so

Applying the Pythagorean Theorem at one triangle

`13^2=(x+7)^2+(2x/2)^2`

solve for x

`169=x^2+14x+49+x^2`

`2x^2+14x-120=0`

solve the quadratic equation by graphing

using a graphing tool

The solution is x=5

see the attached figure

therefore

The length of the base is

`2(5)=10\ units`