Question

find q.

write your answer as a whole number or a decimal. do not round.
q = \boxed{} meters
submit
work it out

Explanation:

Step1: Identify Similar Triangles

Triangles \( CDB \) and \( CEA \) are similar (by AA similarity, as \( \angle CDB = \angle CEA = 90^\circ \) and \( \angle C \) is common). The ratio of corresponding sides in similar triangles is equal. The length of \( CB = 5 \) m and \( CA = CB + BA = 5 + 5 = 10 \) m. So the ratio of similarity is \( \frac{CB}{CA}=\frac{5}{10}=\frac{1}{2} \).

Step2: Apply Proportionality

Since \( \triangle CDB \sim \triangle CEA \), the ratio of \( DB \) (which is \( q \)) to \( EA \) (which is 8 m) is equal to the similarity ratio. So \( \frac{q}{8}=\frac{1}{2} \). Solving for \( q \), we multiply both sides by 8: \( q = 8\times\frac{1}{2}=4 \).

Answer:

\( q = 4 \) meters