Question

If PQR ~ UTV, find the value of x.

Answer 1

The value of x is 15.

Solution:

Given ΔPQR $\sim$ ΔUTV.

If two triangles are similar, then the corresponding parts are congruent.

$\Rightarrow \frac{PR}{UV} =\frac{RQ}{VT}$

$\Rightarrow \frac{14}{x + 6} =\frac{8}{x -3}$

Do cross multiplication, we get

⇒ 14(x - 3) = 8(x + 6)

⇒ 14x - 42 = 8x + 48

Add 42 on both sides.

⇒ 14x = 8x + 90

Subtract 8x on both sides.

⇒ 6x = 90

Divide by 6 on both sides.

⇒ x = 15

The value of x is 15.