Question

What is the value of x? Enter your answer in the box. units

Answer 1

The value of x is 28.

Solution:

Given APR is a triangle.

CD divides the two sides of a triangle APR and CD is parallel to AP.

By Proportionality theorem,

If a parallel line to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.

$\Rightarrow \frac{RC}{CA} =\frac{RD}{DP}$

$\Rightarrow \frac{x}{10} =\frac{42}{15}$

Do cross multiplication.

⇒ 15x = 42 × 10

⇒ 15x = 420

Divide by 15 on both sides of the equation.

⇒ x = 28

The value of x is 28.