Question

use the triangle proportionality theorem to solve for x. 18 x 56 21 65.3 45 48 6.75

Explanation:

Step1: Apply the triangle proportionality theorem

The triangle proportionality theorem states that 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 $\frac{18}{x}=\frac{21}{56}$.

Step2: Cross - multiply

Cross - multiplying gives us $21x = 18\times56$.

Step3: Solve for \(x\)

First, calculate \(18\times56 = 1008\). Then, \(x=\frac{1008}{21}\).
Since \(\frac{1008}{21}=48\).

Answer:

48