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35 votes
In the diagram below of triangle KLM, N is a midpoint of KL and P is a midpoint of LM.If NP = x + 6, and KM = 33 - x, what is the measure of NP? L N Р K M

User Doruk
by
2.7k points

1 Answer

24 votes
24 votes

Answer

x = 7 units

NP = 13 units

KM = 26 units

Explantion

The fact provided that N is a midpoint of KL and P is a midpoint of LM proves that triangle NLP is exactly half the measure of triangle KLM.

And the two triangles are similar to each other.

So, we can see that NP is the corresponding side to KM.

And since KLM = 2 (NLP),

KM = 2 (NP)

KM = 33 - x

NP = x + 6

KM = 2 (NP)

33 - x = 2 (x + 6)

33 - x = 2x + 12

We can rewrite this as

2x + 12 = 33 - x

2x + x = 33 - 12

3x = 21

Divide both sides by 3

(3x/3) = (21/3)

x = 7

NP = x + 6 = 7 + 6 = 13 units

KM = 33 - x = 33 - 7 = 26 units

Hope this Helps!!!

User Clarity
by
3.2k points
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