Question

quiz 4: proportions
what is the value of x in the figure below?
figure of a triangle with segments 9, 24, x, 12 and a right angle-like mark
options: 4.5, 10, 5, none of the choices are correct

Explanation:

Step1: Identify Similar Triangles

The figure shows two triangles with a common angle and right angles (implied by the altitude), so they are similar by AA (Angle - Angle) similarity.

Step2: Set Up Proportion

For similar triangles, the ratios of corresponding sides are equal. So, $\frac{9}{24}=\frac{x}{12}$.

Step3: Solve for \(x\)

Cross - multiply: \(24x = 9\times12\). Then \(24x=108\). Divide both sides by 24: \(x=\frac{108}{24}=4.5\).

Answer:

4.5