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

(Note: Since the diagram is not provided, this question assumes a visual reference is available to the reader.)

Answer :

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

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