Question

The diagram below shows a pennant in the shape of an isosceles triangle. The equal sides each measure 13, the altitude is x+7, and the base is 2x. 13 x + 7 2x 13 What is the length of the base? Your answer

Answer 1

we have that

the altitude divide the isosceles triangle into two congruent right triangles

so

Applying the Pythagorean Theorem

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

solve for x

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

simplify

14x+49=169

14x=169-49

14x=120

x=120/14

simplify

x=60/7

Find the length of the base

2x=2(60/7)=120/7

answer is 120/7 units