Quadrilateral GHIJ is similar to quadrilateral KLMN. Find the measure of side NK. Round your answer to the nearest tenth if necessary.
G
H
I
J
K
L
M
N
28
19.1
5
Answer
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I apologize for the mistake. Let's try solving it again using the correct corresponding sides of the similar quadrilaterals.
Given:
Side GH = 28
Side HI = 19.1
Side KJ = 5
We want to find side NK.
Since the quadrilaterals GHIJ and KLMN are similar, we can set up a proportion using the corresponding sides:
GH/HK = HI/KI
Substitute the given values:
28/5 = 19.1/NK
Solve for NK:
28 * NK = 5 * 19.1
28 * NK = 95.5
NK = 95.5 / 28
NK ≈ 3.41
Therefore, the measure of side NK is approximately 3.4.
To find the length of side NK, we can use the corresponding sides of similar triangles GHI and KLM.
Using the ratio of corresponding sides:
GK/GH = KL/HI
Substitute the given values:
NK/28 = 5/19.1
Cross multiply:
19.1 * NK = 5 * 28
19.1 * NK = 140
NK = 140 / 19.1
NK ≈ 7.33
Therefore, the measure of side NK is approximately 7.3.