Question

how long is the side labeled x? a 5 15 c b 10 d 10 x e 20 f 25 units 35 units 30 units 20 units

Explanation:

Step1: Check for similar triangles

The ratios of corresponding sides of \(\triangle ABC\) and \(\triangle DEF\) are \(\frac{DE}{AB}=\frac{10}{5} = 2\), \(\frac{EF}{BC}=\frac{20}{10}=2\). So the triangles are similar.

Step2: Find the length of \(x\)

Since the triangles are similar, the ratio of the hypotenuses is also 2. Given the hypotenuse of \(\triangle ABC\) is 15, then \(x = 15\times2=30\).

Answer:

C. 30 units