Question

use the image to answer the question
if ( \triangle abcsim\triangle xby ), and ( overline{ab}=16mathrm{cm},overline{ac}=8mathrm{cm} ), and ( overline{xy}=6mathrm{cm} ), then what is the length of ( overline{bx} )?
(1 point)
( overline{bx}=squaremathrm{cm} )

Explanation:

Step1: Use the property of similar triangles

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

Step2: Substitute the given values

We know \(AB = 16\mathrm{cm}\), \(AC = 8\mathrm{cm}\), and \(XY=6\mathrm{cm}\). Substituting into \(\frac{AB}{XB}=\frac{AC}{XY}\), we get \(\frac{16}{XB}=\frac{8}{6}\).

Step3: Solve for \(XB\)

Cross - multiply: \(8\times XB=16\times6\). Then \(XB=\frac{16\times6}{8}\).

Answer:

\(12\)