Question

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

Explanation:

Step1: Identify similar triangles

Triangles \( \triangle GIH \) and \( \triangle JIK \) are similar (by AA similarity, as corresponding angles are equal).

Step2: Set up proportion

For similar triangles, the ratios of corresponding sides are equal. So, \( \frac{GI}{JI} = \frac{IH}{IK} \). Given \( GI = 4 \) ft, \( JI = 8 \) ft, \( IH = 3 \) ft, and \( IK = w \) ft. Substituting values: \( \frac{4}{8} = \frac{3}{w} \).

Step3: Solve for \( w \)

Cross - multiply: \( 4w = 8\times3 \). Then \( 4w = 24 \). Divide both sides by 4: \( w=\frac{24}{4}=6 \).

Answer:

\( w = 6 \)