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:
The correct option is B.
Step-by-step 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.