Question

triangle ghi is similar to triangle jkl. find the measure of side jk. round your answer to the nearest tenth if necessary. i 17 h l 54 k g 31 j

Explanation:

Step1: Identify Corresponding Sides

In similar triangles \( \triangle GHI \) and \( \triangle JKL \), the sides \( HI \) and \( KL \), \( GH \) and \( JK \) are corresponding. So, the ratios of corresponding sides are equal: \( \frac{HI}{KL}=\frac{GH}{JK} \).

Step2: Substitute Values

Given \( HI = 17 \), \( KL = 54 \), \( GH = 31 \), substitute into the proportion: \( \frac{17}{54}=\frac{31}{JK} \).

Step3: Solve for \( JK \)

Cross - multiply: \( 17\times JK = 54\times31 \). Calculate \( 54\times31 = 1674 \). Then \( JK=\frac{1674}{17}\approx98.5 \).

Answer:

\( 98.5 \)