in the diagram below of triangle MNP, Q is a midpoint of MN and R is a midpoint of NP . if QR = 11-x, and MP=57-7x, what is the measure of MP?

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Given:

Given that MNP is a triangle. Q is the midpoint of MN and R is the midpoint of NP.

The length of QR is 4x -11 and the length of MP is 9x - 29.

We need to determine the measure of MP.

Value of x:

The value of x can be determined using the triangle midsegment theorem.

Applying the theorem, we have;

Substituting the lengths, we get;

Subtracting both sides by 8x, we have;

Adding both sides of the equation by 29, we get;

Thus, the value of x is 7.

Measure of MP:

The measure of MP can be determined by substituting x = 7 in the length of MP.

Thus, we have;

Thus, the measure of MP is 34.

Step-by-step explanation:

1/3 + 1/5 = 8/15.

step-by-step explanation:

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