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

The correct option is;

C: 10.5 inches

Step-by-step explanation:

In triangle ΔPQR the given parameters are;

The length of = 19.5 in.

The length of = 7.5 in.

In triangle ΔVWX, the given parameters are;

The length of = 13 in.

The length of = 5 in.

The length of = 7 in.

Given that we have;

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, and ;

∴ = 7 × 1.5 = 10.5

The length of = 10.5 inches

step-by-step explanation:

this can be solved first with pythagorean theorem, which tells us to square both legs of the triangle and sum it. this will be equal to the square of the hypotenuse.

the hypotenuse is the side "opposite" the 90 degree angle, which is x.

so we can write using pythagorean theorem,

simplifying:

to further simplify this radical, we need to use the property  

thus