Question

given the two similar triangles below determine the value of side lj, given that side kl is 9 ft. 10 g k 15 ft h l 20 ft 10 ft j lj=

Explanation:

Step1: Set up proportion

Since the triangles are similar, the ratios of corresponding sides are equal. Let the side corresponding to $IJ$ be $FH$. The ratio of $KL$ to $GH$ is equal to the ratio of $LJ$ to $FH$. So we have $\frac{KL}{GH}=\frac{LJ}{FH}$.

Step2: Substitute known values

We know that $KL = 9$ ft, $GH=15$ ft and $FH = 10$ ft. Substituting these values into the proportion $\frac{9}{15}=\frac{LJ}{10}$.

Step3: Solve for $LJ$

Cross - multiply: $15\times LJ=9\times10$. Then $15LJ = 90$. Divide both sides by 15: $LJ=\frac{90}{15}=6$ ft.

Answer:

$6$ ft