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

Question

2 years ago

8

that LMNO is a parallelogram.. . A.24. B.48. C.61. D.122

2 answers:

salantis [7] · Answer 1 · 2022-08-07T10:52:24+03:00

8 0

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

Zina [86] · Answer 2 · 2022-08-07T13:11:12+03:00

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.