Question

Proving Similar Triangles Quick Check 1 of 51 of 5 Items Question Use the image to answer the question. △JKL∼△PKQ , and KP¯¯¯¯¯¯¯¯=14 m, JK¯¯¯¯¯¯¯¯=56 m, and KQ¯¯¯¯¯¯¯¯=21 m. What is the length of KL¯¯¯¯¯¯¯¯ ? (1 point) Responses 84 m 84 m 72 m 72 m 34 m 34 m 5.25 m 5.25 m Skip to navigation page 23 of 23 Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.

Answer 1

To determine the length of $KL$ in the similar triangles $\mathrm{△}JKL$ and $\mathrm{△}PKQ$, we can use the property of similar triangles, which states that corresponding sides are proportional.

Given:

• $KP=14$ m
• $JK=56$ m
• $KQ=21$ m

We need to find the length of $KL$. Since the triangles are similar, we can set up the following proportion based on corresponding sides:

$$\frac{JK}{KP}=\frac{KL}{KQ}$$

Substituting the known values into the proportion:

$$\frac{56}{14}=\frac{KL}{21}$$

Calculating the left side:

$$\frac{56}{14}=4$$

So we have:

$$4=\frac{KL}{21}$$

To solve for $KL$, multiply both sides by $21$:

$$KL=4\times 21=84\text{ m}$$

Therefore, the length of $KL$ is $84$ m.

Final Answer: 84 m