Question

$\triangle abc$ is similar to $\triangle xyz$. $ab$ is 9 feet and $bc$ is 12 feet while $xy$ is 3 feet. then what length is $yz$?
enter the value. you do not need to enter the units. round to the nearest tenth if necessary.

Explanation:

Step1: Set up the proportion

Since \(\triangle ABC\sim\triangle XYZ\), the ratios of corresponding sides are equal. So, \(\frac{AB}{XY}=\frac{BC}{YZ}\).

Step2: Substitute the known values

We know \(AB = 9\), \(XY=3\), and \(BC = 12\). Substituting these into the proportion gives \(\frac{9}{3}=\frac{12}{YZ}\).

Step3: Cross - multiply

Cross - multiplying gives \(9\times YZ=3\times12\).

Step4: Solve for \(YZ\)

First, calculate \(3\times12 = 36\). Then, \(9YZ=36\), so \(YZ=\frac{36}{9}\).

Answer:

\(4\)