Question

find v.
write your answer as a whole number or a decimal. do not round.
v = \boxed{} feet

Explanation:

Step1: Identify similar triangles

Triangles \( \triangle IJH \) and \( \triangle KGH \) are similar (by AA similarity, as they have right angles and share the angle at \( H \)).

Step2: Set up proportion

For similar triangles, the ratios of corresponding sides are equal. So, \( \frac{IJ}{KG} = \frac{JH}{GH} \). Substituting the known values: \( IJ = 6 \) ft, \( KG = 3 \) ft, \( JH = 8 \) ft, \( GH = v \) ft. The proportion becomes \( \frac{6}{3} = \frac{8}{v} \).

Step3: Solve for \( v \)

Cross - multiply: \( 6v = 3\times8 \). So, \( 6v = 24 \). Divide both sides by 6: \( v=\frac{24}{6}=4 \).

Answer:

\( v = 4 \) feet