Question

if the figures below are similar, find the value of x.
28.
29.
use the given information to find each measure.

1. given \\( \triangle c d e \sim \triangle k l m \\), find \\( d e \\).
2. given \\( \triangle q r s \sim \triangle q t v \\), find \\( r s \\).

Explanation:

28.

Step1: Set up proportion

Since the trapezoids are similar, the ratios of corresponding sides are equal. So, \(\frac{18}{30}=\frac{14}{x}\).

Step2: Cross - multiply

\(18x = 14\times30\).

Step3: Solve for \(x\)

\(18x=420\), then \(x=\frac{420}{18}=\frac{70}{3}\approx23.33\).

Step1: Set up proportion

Because the triangles are similar (by AA similarity, vertical angles are equal and two pairs of corresponding angles are equal), \(\frac{10.5}{x}=\frac{13.3}{15}\).

Step2: Cross - multiply

\(13.3x=10.5\times15\).

Step3: Solve for \(x\)

\(13.3x = 157.5\), then \(x=\frac{157.5}{13.3}=\frac{1575}{133}\approx11.84\).

Step1: Set up proportion

Since \(\triangle CDE\sim\triangle KLM\), \(\frac{DE}{LM}=\frac{CE}{KM}\). Let \(DE = y\), then \(\frac{y}{12}=\frac{15}{8}\).

Step2: Cross - multiply

\(8y=12\times15\).

Step3: Solve for \(y\)

\(8y = 180\), then \(y=\frac{180}{8}=\frac{45}{2}=22.5\).

Answer:

\(x = \frac{70}{3}\)

29.