Question

solve for ( x ). figures are not necessarily drawn to scale.
(image of a right triangle ( klm ) with right angle at ( l ), and a smaller right triangle ( onm ) inside it, with ( lo = 6 ), ( om = 8 ), ( lm = 17.6 ), and ( kl = x ))

Explanation:

Step1: Identify Similar Triangles

Triangles \( KLM \) and \( ONM \) are similar (right triangles with a common angle at \( M \), so by AA similarity).

Step2: Set Up Proportion

Let \( LO = 17.6 - 8 = 9.6 \). The ratio of corresponding sides in similar triangles is equal. So, \(\frac{KL}{ON}=\frac{LM}{OM}\). Substituting values: \(\frac{x}{6}=\frac{17.6}{8}\).

Step3: Solve for \( x \)

Cross - multiply: \( 8x = 6\times17.6 \). Calculate \( 6\times17.6 = 105.6 \). Then, \( x=\frac{105.6}{8}=13.2 \).

Answer:

\( x = 13.2 \)