Question

in the diagram below, \\( \triangle cde \sim \triangle cfg \\). find \\( j \\).
write your answer as a whole number or a decimal. do not round.
\\( j= \\) meters

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle CDE\sim\triangle CFG\), the ratios of corresponding sides are equal. That is \(\frac{CD}{CF}=\frac{DE}{FG}\).
Here, \(CD = 3\)m, \(DE=2\)m, \(FG = 4\)m, and \(CF=j\).
Substituting the values into the proportion: \(\frac{3}{j}=\frac{2}{4}\).

Step2: Cross - multiply and solve for \(j\)

Cross - multiplying gives \(2j=3\times4\).
So, \(2j = 12\).
Dividing both sides by 2: \(j=\frac{12}{2}\).

Answer:

\(j = 6\) meters