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

The correct option is;

C: 10.5 inches

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;

`\frac{\overline {QP}}{\overline {WV}} = (19.5)/(13) = 1.5 , \ \frac{\overline {QR}}{\overline {WX}} = (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}`;

`\frac{\overline {PR}}{\overline {WV}} = \frac{\overline {PR}}{\overline {7}} = 1.5`

∴
`\overline {PR}` = 7 × 1.5 = 10.5

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