Question

In the diagram below of triangle MNP, Q is the midpoint of MN and R is a midpoint of NP. If QR=4x-11 , and MP=9x-29 , what is the measure of MP?

Answer 1

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;

$MP=2(QR)$

Substituting the lengths, we get;

$9x-29=2(4x-11)$

$9x-29=8x-22$

Subtracting both sides by 8x, we have;

$x-29=-22$

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

$x=7$

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;

$MP= 9(7) - 29$

$MP=63- 29$

$MP=34$

Thus, the measure of MP is 34.

Answer 2

Answer:

34

Step-by-step explanation:

MP = 2QR

9x - 29 = 2(4x - 11)

9x - 29 = 8x - 22

x = 7

MP = 9(7) - 29

63 - 29

34