The value of x is 28
Explanation:
Given that APR is a triangle with line segment CD parallel to AP.
It is also given that AC = 10. CR = x. PD = 15. DR = 42
The image of the triangle showing these measurement is attached below.
The triangle proportionality theorem states that, "If a line is drawn parallel to one side of a triangle, it intersects the other two sides and divides them proportionally.
Hence, we have,
[tex]\frac{R C}{C A}=\frac{R D}{D P}[/tex]
Now, we shall substitute the values, we get,
[tex]\frac{x}{10}=\frac{42}{15}[/tex]
Multiplying both sides by 10, we have,
[tex]x=10\left(\frac{42}{15}\right)[/tex]
Simplifying, we get,
[tex]x=\frac{420}{15}[/tex]
Dividing,
[tex]x=28[/tex]
Thus, the value of x is 28.
