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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.
Explanation: