Question

ΔABC and ΔXYZ are similar triangles. If BC = x + 7, AC = x + 6, YZ = 4 − x, and XZ = 3 − x, find the value of x.

Answer 1

-3/2 or -1.5

Explanation:

-3/2 = -1.5

BC = -1.5 + 7 = 5.5

AC = -1.5 + 6 = 4.5

YZ = 4 - (-1.5) = 5.5

XZ = 3 - (-1.5) = 4.5

Answer 2

Since these triangles are similar, we have proportional sides. We can write that
`(x+7)/(4-x) = (x+6)/(3-x)`. Solving it, we find that x=-1.5