Question

in the figure above, $\triangle ihj \sim \triangle lkj$, $\overline{ij} = 2$, $\overline{jh} = 3$, $\overline{jl} = 7$.
determine the following:
$\overline{jl} : \overline{ij} = $ answer
$\overline{kj} = $ answer

Explanation:

First Sub - Question: $\boldsymbol{\overline{JL}:\overline{IJ}}$

Step1: Identify the values of $\overline{JL}$ and $\overline{IJ}$

We are given that $\overline{JL} = 7$ and $\overline{IJ}=2$.

Step2: Find the ratio $\overline{JL}:\overline{IJ}$

The ratio of two lengths $a$ and $b$ is given by $\frac{a}{b}$. So, for $\overline{JL}$ and $\overline{IJ}$, the ratio $\overline{JL}:\overline{IJ}$ is $\frac{\overline{JL}}{\overline{IJ}}=\frac{7}{2}$.

Second Sub - Question: $\boldsymbol{\overline{KJ}}$

Step1: Recall the property of similar triangles

Since $\triangle IHJ\sim\triangle LKJ$, the corresponding sides of similar triangles are proportional. That is, $\frac{\overline{JL}}{\overline{IJ}}=\frac{\overline{KJ}}{\overline{JH}}$.

Step2: Substitute the known values

We know that $\overline{JL} = 7$, $\overline{IJ}=2$, and $\overline{JH}=3$. Substituting these values into the proportion $\frac{7}{2}=\frac{\overline{KJ}}{3}$.

Step3: Solve for $\overline{KJ}$

To solve for $\overline{KJ}$, we can cross - multiply. So, $2\times\overline{KJ}=7\times3$. Then $\overline{KJ}=\frac{21}{2} = 10.5$.

Answer:

s:

• $\overline{JL}:\overline{IJ}=\frac{7}{2}$
• $\overline{KJ}=\frac{21}{2}$ (or $10.5$)