Question

in the figure below, \\( \triangle abc \\) is similar to \\( \triangle xyz \\). what is the length of \\( zx \\)? enter only the number as an integer or decimal.
the solution is

Explanation:

Step1: Use the property of similar triangles

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

We know \(AB = 2\), \(XY=7\), \(BC = 4\), and we need to find \(YZ\).

Step2: Set up the proportion

\(\frac{2}{7}=\frac{4}{YZ}\)

Cross - multiply: \(2\times YZ=7\times4\)

\(2YZ = 28\)

Step3: Solve for \(YZ\)

Divide both sides by 2: \(YZ=\frac{28}{2}=14\)

Answer:

\(14\)