Question

name______
date______
(there are two triangles, the left triangle has a side labeled x and a vertical side labeled 1, the right triangle has a hypotenuse labeled 9 and a vertical side labeled 3)

Explanation:

Step1: Identify similar triangles

The two triangles are similar (same angle, so sides are proportional). Let the sides of the first triangle be \( x \), \( 1 \), and the base, and the second triangle be \( 9 \), \( 3 \), and its base. The ratio of corresponding sides should be equal. So, \(\frac{x}{9}=\frac{1}{3}\).

Step2: Solve for \( x \)

Cross - multiply: \( 3x = 9\times1 \). Then, \( 3x=9 \). Divide both sides by 3: \( x=\frac{9}{3}=3 \).

Answer:

\( x = 3 \)