Question

use the triangle proportionality theorem to calculate the value of x.
x =

Explanation:

Step1: Apply the triangle proportionality theorem

According to the triangle proportionality theorem, if a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally. So, we have the proportion \(\frac{16}{20}=\frac{x + 5}{30}\).

Step2: Cross - multiply

Cross - multiplying gives \(16\times30=20\times(x + 5)\).

$$
LATEXBLOCK0
$$

Step3: Solve for \(x\)

Subtract \(100\) from both sides: \(480-100 = 20x\), so \(380=20x\). Then divide both sides by \(20\): \(x=\frac{380}{20}=19\).

Answer:

\(19\)