Question

given two similar triangles, \\( \triangle abc \sim \triangle def \\), where, \\( d = 5 \\), \\( e = 2.5 \\), \\( b = 7.5 \\), find \\( a \\).
if necessary, round to the tenths place.

Explanation:

Step1: Use the property of similar triangles

For similar triangles \(\triangle ABC\sim\triangle DEF\), the ratios of corresponding sides are equal. So, \(\frac{a}{d}=\frac{b}{e}\).

Step2: Substitute the given values

Substitute \(d = 5\), \(e=2.5\), and \(b = 7.5\) into the proportion \(\frac{a}{5}=\frac{7.5}{2.5}\).

Step3: Solve for \(a\)

Cross - multiply: \(2.5a=5\times7.5\). Then \(2.5a = 37.5\). Divide both sides by \(2.5\): \(a=\frac{37.5}{2.5}=15\).

Answer:

\(15\)