Question

The diagonals of parallelogram LMNO, LN and MO intersect at point P. If LP=7, MP = 5x-10, and OP = 2x + 2, solve for x.

A. 8/3

B. 17/5

C. 4

D. 7

Answer 1

C.

Explanation:

Answer 2

Recall that one of the properties of a parallelogram is that the diagonals bisect each other. That is diagonal LN and MO bisect each other at point P.

Thus, LP = NP and MP = OP

Given that MP = 5x - 10 and OP = 2x + 2

This means that 5x - 10 = 2x + 2
5x - 2x = 2 + 10
3x = 12
x = 12 / 3
x = 4.

Therefore, the value of x is 4.