Question

find d.
h
16 ft
g
d
i
6 ft
j
6 ft
k
write your answer as a whole number or a decimal. do not round.
d = feet
submit

Explanation:

Step1: Identify Similar Triangles

Triangles \( \triangle HIK \) and \( \triangle GJK \) are similar (both right - angled, share \( \angle K \)). So, the ratios of corresponding sides are equal.

Step2: Determine Side Lengths

The length of \( IK=IJ + JK=6 + 6 = 12\) ft, \( JK = 6\) ft, and \( HI = 16\) ft. Let \( GJ=d\). Since the triangles are similar, \( \frac{GJ}{HI}=\frac{JK}{IK}\).

Step3: Substitute Values and Solve

Substitute \( GJ = d\), \( HI = 16\), \( JK = 6\), and \( IK = 12\) into the proportion: \( \frac{d}{16}=\frac{6}{12}\). Cross - multiply: \( 12d=16\times6\). Then \( 12d = 96\). Divide both sides by 12: \( d=\frac{96}{12}=8\).

Answer:

8