Question

triangle hij is similar to triangle klm. find the measure of side kl. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Set up the proportion

Since the triangles are similar, the ratios of corresponding sides are equal. Let \( KL = x \). The proportion is \(\frac{IJ}{LM}=\frac{HI}{KL}\). Substituting the values: \(\frac{9}{41}=\frac{7.5}{x}\).

Step2: Cross - multiply

Cross - multiplying gives \(9x = 7.5\times41\).

Step3: Calculate the right - hand side

\(7.5\times41 = 307.5\). So, \(9x=307.5\).

Step4: Solve for \(x\)

Divide both sides by 9: \(x=\frac{307.5}{9}\).
\(x = 34.166\cdots\approx34.2\).

Answer:

\(34.2\)