Question

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In the diagram below of triangle MNO, P is the midpoint of MO and Q is the
midpoint of NO.If PQ = 49 – 8x, and MN = 41 + 3x, what is the measure of
MN?
O
N
P
M M

Answer 1

MN = 50

Explanation:

Given:

PQ = 49 – 8x

MN = 41 + 3x

Required:

Measure of MN

Solution:

PQ = ½(MN) => Mid-segment theorem of a triangle

Substitute

49 - 8x = ½(41 + 3x)

Multiply both sides by 2

2(49 - 8x) = 41 + 3x

98 - 16x = 41 + 3x

Collect like terms

98 - 41 = 16x + 3x

57 = 19x

57/19 = 19x/19

3 = x

x = 3

Find MN:

MN = 41 + 3x

Plug in the value of x

MN = 41 + 3(3) = 41 + 9

MN = 50