Question

What is the length of PR? A: 13.5 inches B: 7.5 inches C: 10.5 inches D: 9.5 inches

Answer 1

Answer:

The correct option is;

C: 10.5 inches

Step-by-step explanation:

In triangle ΔPQR the given parameters are;

The length of $\overline {QP}$ = 19.5 in.

The length of $\overline {QR}$ = 7.5 in.

In triangle ΔVWX, the given parameters are;

The length of $\overline {WV}$ = 13 in.

The length of $\overline {WX}$ = 5 in.

The length of $\overline {VX}$ = 7 in.

Given that we have;

$\dfrac{\overline {QP}}{\overline {WV}} = \dfrac{19.5}{13} = 1.5 , \ \dfrac{\overline {QR}}{\overline {WX}} = \dfrac{7.5}{5} = 1.5$

The ratio of the corresponding sides of triangle ΔPQR and triangle ΔVWX are equal, therefore ΔPQR is similar to ΔVWX, from which we have for the corresponding sides, $\overline {PR}$ and $\overline {VX}$;

$\dfrac{\overline {PR}}{\overline {WV}} = \dfrac{\overline {PR}}{\overline {7}} = 1.5$

∴ $\overline {PR}$ = 7 × 1.5 = 10.5

The length of $\overline {PR}$ = 10.5 inches