Question

in the diagram to the right, \\( \triangle hkm - \triangle dfg \\).
find \\( \frac { g d } { m h } \\)
\\( \frac { g d } { m h } = \\) (type an integer or a simplified fraction.)

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle HKM\sim\triangle DFG\), the ratios of corresponding sides are equal. That is \(\frac{GD}{MH}=\frac{DF}{HK}=\frac{FG}{KM}=\frac{DG}{HM}\)

Step2: Identify the corresponding sides

We know that \(DF = 105\) and \(HK=25\)

Step3: Calculate the ratio

\(\frac{GD}{MH}=\frac{DF}{HK}\)

Substitute \(DF = 105\) and \(HK = 25\) into the formula: \(\frac{GD}{MH}=\frac{105}{25}=\frac{21}{5}\)

Answer:

\(\frac{21}{5}\)