Question

ΔABC and ΔXYZ are similar triangles. If BA = x + 9, AC = x + 7, YX = x + 5, and XZ = x + 4, find the value of x.

Answer 1

Answer:

-1

Step-by-step explanation:

Answer 2

Solution:

we are given that ΔABC and ΔXYZ are similar triangles.

As we know , when two triangles are similar then the ratios of their corrsponding sides are equal.

Here we have

BA = x + 9, AC = x + 7, YX = x + 5, and XZ = x + 4

So we can write

$\frac{x+9}{x+5}= \frac{x+7}{x+4}\\ \\ (x+9)(x+4)=(x+7)(x+5)\\ \\ x^2+13x+36=x^2+12x+35\\ \\ 13x-12x=35-36\\ \\ x=-1$

Hence then value of x=-1.