Question

find y.

write your answer as a whole number or a decimal. do not round.

y = \boxed{} meters

submit
work it out
not feeling ready yet? these can help:
side lengths and angle measures in similar figures
lesson: similar triangles

Explanation:

Step1: Identify similar triangles

Triangles \( \triangle DCF \) and \( \triangle EGF \) are similar (AA similarity, right angles and common angle at \( F \)).

Step2: Set up proportion

The ratio of corresponding sides is equal. So, \( \frac{DE + EF}{EF}=\frac{DC}{EG} \), which is \( \frac{17 + 34}{34}=\frac{24}{y} \). Simplify \( \frac{51}{34}=\frac{24}{y} \).

Step3: Solve for \( y \)

Cross - multiply: \( 51y=34\times24 \). Then \( y = \frac{34\times24}{51} \). Calculate \( 34\times24 = 816 \), and \( \frac{816}{51}=16 \).

Answer:

16