Chapter 8, Problem 27RP

To determine

To calculate:The sum of two sides of a triangle i.e. NR and NS.

Answer to Problem 27RP

The sum of the sides is 20.8 units.

Explanation of Solution

Given information:

Two lines are parallel and

NP = 5x − 21, PR = 5, NT = x, TS = 8

Formula used:

In similar triangles, ratio of corresponding sides are equivalent

Calculation:

Since, triangles are similar, we have

  $\begin{array}{l}\frac{NP}{NR}=\frac{NT}{NS}\\ \Rightarrow \frac{NP}{NP+PR}=\frac{NT}{NT+TS}\\ \Rightarrow \frac{5x-21}{5x-21+5}=\frac{x}{x+8}\\ \Rightarrow \frac{5x-21}{5x-16}=\frac{x}{x+8}\\ \Rightarrow \left(5x-21\right)\left(x+8\right)=\left(5x-16\right)\left(x\right)\\ \Rightarrow 5x^2+19x-168=5x^2-16x\\ \Rightarrow 35x=168\\ \Rightarrow x=4.8\end{array}$

  $\begin{array}{l}\therefore NR=5x-16=5\times 4.8-16=24-16=8\text{ units}\\ \text{ and }NS=x+8=4.8+8=12.8\\ \text{ Hence},NR+\text{}NS=8+12.8=20.8\text{}\text{ units}\end{array}$