Chapter 6.7, Problem 24STP

To determine

To find: The length of missing side XZ in two given similar triangles RST and XYZ.

Answer to Problem 24STP

Length of side XZ is 4.8 inches.

Explanation of Solution

Given information: 

Following two similar triangles RST and XYZ in which two pairs of corresponding sides are given:

  

Concept used:

In similar triangles, the ratio of corresponding sides as well as of their altitudes are equal always. So, if M and N are foot of perpendicular from points R and X on opposite bases, then in said given similar triangles,

  $\frac{XZ}{RT}=\frac{XN}{RM}$

Calculation: Based on above ratio set,

  $\frac{\text{x}}{8}=\frac{3}{5}$

On cross multiply,

  $x=\frac{3\times 8}{5}=\frac{24}{5}=4.8$

Based on above calculation, the length of missing side XZ is 4.8 inches.