Question

find d.
write your answer as a whole number or a decimal. do not round.
d = meters

Explanation:

Step1: Prove triangle similarity

Since vertical angles are equal and two angles of \(\triangle CDE\) and \(\triangle FGE\) are equal (\(\angle C=\angle G\), \(\angle D=\angle F\)), by the AA (Angle - Angle) similarity criterion, \(\triangle CDE\sim\triangle FGE\).

Step2: Set up proportion

For similar triangles \(\triangle CDE\) and \(\triangle FGE\), the ratios of corresponding sides are equal. So, \(\frac{CD}{FG}=\frac{CE}{FE}\). Let \(CD = 92\), \(CE = 84\), \(FE=63\), and \(FG = d\). Then \(\frac{92}{d}=\frac{84}{63}\).

Step3: Solve for \(d\)

Cross - multiply: \(84d=92\times63\). Then \(d=\frac{92\times63}{84}\). Simplify \(\frac{92\times63}{84}=\frac{92\times3}{4}\) (divide numerator and denominator by 21). And \(\frac{92\times3}{4}= 69\).

Answer:

\(69\)