Question

what is the value of X

Answer 1

The value of x is 25

Explanation:

From the figure, we can see that DBR is a triangle.

The line QC is parallel to the line BR

We need to determine the value of x.

Since, the line QC is parallel to the side of the triangle BR, then by side - splitter theorem, we have,

$\frac{DQ}{QB}=\frac{DC}{CR}$

From the figure, we have, the lengths of the sides $DQ=40$ , $QB=24$ , $CR=15$ and $DC=x$

Substituting these values in the above expression, we have,

$\frac{40}{24}=\frac{x}{15}$

Multiplying both sides of the expression by 15, we get,

$\frac{40\times 15}{24}=x$

Simplifying, we get,

$\frac{600}{24} =x$

Dividing, we get,

$25=x$

Thus, the value of x is 25

Therefore, the length of DC is 25