Answer:
The correct option is;
C: 10.5 inches
Step-by-step explanation:
In triangle ΔPQR the given parameters are;
The length of [tex]\overline {QP}[/tex] = 19.5 in.
The length of [tex]\overline {QR}[/tex] = 7.5 in.
In triangle ΔVWX, the given parameters are;
The length of [tex]\overline {WV}[/tex] = 13 in.
The length of [tex]\overline {WX}[/tex] = 5 in.
The length of [tex]\overline {VX}[/tex] = 7 in.
Given that we have;
[tex]\dfrac{\overline {QP}}{\overline {WV}} = \dfrac{19.5}{13} = 1.5 , \ \dfrac{\overline {QR}}{\overline {WX}} = \dfrac{7.5}{5} = 1.5[/tex]
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, [tex]\overline {PR}[/tex] and [tex]\overline {VX}[/tex];
[tex]\dfrac{\overline {PR}}{\overline {WV}} = \dfrac{\overline {PR}}{\overline {7}} = 1.5[/tex]
∴ [tex]\overline {PR}[/tex] = 7 × 1.5 = 10.5
The length of [tex]\overline {PR}[/tex] = 10.5 inches
