Question

What is the value of x? Enter your answer in the box. units Triangle A P R with line segment C D parallel to segment A P with C between A and R and D between P and R. A C equals 10. C R equals x. P D equals 15. D R equals 42.

Answer 1

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,

$\frac{R C}{C A}=\frac{R D}{D P}$

Now, we shall substitute the values, we get,

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

Multiplying both sides by 10, we have,

$x=10\left(\frac{42}{15}\right)$

Simplifying, we get,

$x=\frac{420}{15}$

Dividing,

$x=28$

Thus, the value of x is 28.