Question

in the diagram below, \\( \triangle edc \sim \triangle bda \\). find \\( g \\).
write your answer as a whole number or a decimal. do not round.

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle EDC\sim\triangle BDA\), the ratios of their corresponding sides are equal. That is \(\frac{ED}{BD}=\frac{DC}{DA}\).

Step2: Substitute the known values

We know \(ED = 4\), \(DC=3\), \(DA = 5\). Let \(BD = g\). Then \(\frac{4}{g}=\frac{3}{5}\).

Step3: Solve for \(g\)

Cross - multiply gives \(3g=4\times5\), so \(3g = 20\), and \(g=\frac{20}{3}\approx6.7\).

Answer:

\(6.7\)