Question

In ∆XYZ, if ∠X ≅ ∠Z , XY = 13x – 21, YZ = 8x – 6, and XZ = x + 4, find the value of x and the measure of each side.

Answer 1

Explanation:

when 2 angles in a triangle have the same size, this triangle is an isoceles triangle with both legs being equally long, and the side connecting the equal angles being the baseline.

in our example here

XZ is therefore the baseline.

and then XY and YZ are the equal legs :

13x - 21 = 8x - 6

5x - 21 = -6

5x = 15

x = 3

XY = 13×3 - 21 = 39 - 21 = 18

YZ = 8×3 - 6 = 24 - 6 = 18

XZ = 3 + 4 = 7