Question

in the diagram below, $\triangle lkj \sim \triangle ihj$. find $s$.

(diagram: triangle $ihj$ with $h$ to $i$ labeled $s$, $i$ to $j$ labeled 96 m. triangle $lkj$ with $l$ to $k$ labeled 46 m, $l$ to $j$ labeled 48 m. the triangles intersect at $j$.)

write your answer as a whole number or a decimal. do not round.

$s = \square$ meters

Explanation:

Step1: Recall Similar Triangles Property

Since \(\triangle LKJ \sim \triangle IHJ\), the corresponding sides are proportional. So, \(\frac{LK}{IH}=\frac{LJ}{IJ}\).

Step2: Identify Corresponding Sides

We know \(LK = 46\) m, \(LJ = 48\) m, and \(IJ = 96\) m. Let \(IH = s\).

Step3: Set Up Proportion

Substitute the values into the proportion: \(\frac{46}{s}=\frac{48}{96}\).

Step4: Solve for \(s\)

Cross - multiply: \(48s=46\times96\). Then, \(s = \frac{46\times96}{48}\). Simplify \(\frac{96}{48}=2\), so \(s = 46\times2=92\).

Answer:

92