Chapter 6.9, Problem 2GP

To determine

To find: The missing distance x between cabin and the mess hall, in two similar triangles QRS and URT given.

Answer to Problem 2GP

Required distance between the cabin and the mess hall is 180 yards.

Explanation of Solution

Given information:

Following two similar triangles QRS and URT in which two pairs of corresponding sides are given:

  

Concept used:

In similar triangles, ratio of corresponding sides are equal always. So, in given similar triangles,

  $\frac{\text{QR}}{\text{RU}}=\frac{\text{SR}}{\text{RT}}$

Calculation: So, based on above ratio set,

  $\frac{\text{x}}{60}=\frac{138}{46}$

On cross multiply,

  $x=\frac{138\times 60}{46}=60\times 3=180$

Based on above calculation, the distance x between the cabin and mass hall is calculated as 180 yards.