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 \( \triangle JKL \) and \( \triangle PKQ \), 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