Chapter 8.1, Problem 25PSC

To determine

To calculate: The length of line segment if a line is divided by a given point “ P ” externally as shown in the figure.

Answer to Problem 25PSC

The length of the line segment will be 75 units

Explanation of Solution

Given information:

P is said to be divide $\overline{\text{AB}}$ externally into two segments $\overline{\text{AP}}\&\overline{\text{PB}}$

Also, given that

AB = 30 and $\frac{\text{AP}}{\text{AB}}=\frac{5}{2}$

Formula used:

On subtracting ‘1’ from the equivalent ratios, value remains unchanged

Calculation

.Given

  $\begin{array}{l}\frac{\text{AP}}{\text{AB}}=\frac{5}{2}\\ \Rightarrow \frac{\text{AP}}{\text{AB}}-1=\frac{5}{2}-1\\ \Rightarrow \frac{\text{AP}-\text{AB}}{\text{AB}}=\frac{5-2}{2}\\ \Rightarrow \frac{\text{AP}-30}{30}=\frac{3}{2}\\ \Rightarrow \text{AP}-30=\frac{3}{2}\times 30=45\\ \Rightarrow \text{AP = 45+30}\\ \Rightarrow \text{AP = 75 units}\end{array}$