Question

Quadrilateral LMNO has diagonals that intersect at point P. If LP=NP, MP = y + 25, and OP = 5y + 29, find the length of MO such that LMNO is a parallelogram.. . A.24. B.48. C.61. D.122

Answer 1

the right  answer will be  c.61 that is your answer

Answer 2

The correct option is B.

Explanation:

Given information: LMNO is a parallelogram, LMNO has diagonals that intersect at point P, LP=NP, MP = y + 25, and OP = 5y + 29.

Diagonals of parallelogram bisects each other.

Since P is the intersection point of diagonal and MO is a diagonal, so

`MP=OP`

`y+25=5y+29`

Subtract y from both the sides.

`y+25-y=5y+29-y`

`25=4y+29`

Subtract 29 from both the sides.

`25-29=4y+29-29`

`-4=4y`

Divide both sides by 4.

`-1=y`

The value of y is -1.

The length of MO is

`MO=MP+OP`

`MO=y+25+5y+29`

`MO=6y+54`

Substitute y=-1 in the above equation.

`MO=6(-1)+54`

`MO=-6+54`

`MO=48`

The length of MO is 48. Therefore the correct option is B.