Question

in the figure below, \\( \triangle a b c \\) is similar to \\( \triangle x y z \\). what is the length of \\( \overline{x y} \\)? 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 \(\frac{AB}{XY}=\frac{AC}{XZ}=\frac{BC}{YZ}\). We can use \(\frac{BC}{YZ}=\frac{AB}{XY}\).

Step2: Substitute the known values

We know \(BC = 12\), \(YZ=27\), \(AB = 5\). Let \(XY=x\). Then \(\frac{12}{27}=\frac{5}{x}\).

Step3: Cross - multiply

Cross - multiplying gives \(12x=27\times5\). So \(12x = 135\).

Step4: Solve for \(x\)

Divide both sides by 12: \(x=\frac{135}{12}=\frac{45}{4}=11.25\).

Answer:

\(11.25\)