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.
[tex]$\Rightarrow \frac{RC}{CA} =\frac{RD}{DP}[/tex]
[tex]$\Rightarrow \frac{x}{10} =\frac{42}{15}[/tex]
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.
