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Quadrilateral LMNO has diagonals that intersect at point P. If , LP = 6x – 5, and NP = 4x + 17, find the length of / such that LMNO is a parallelogram.

2 Answers

4 votes

Answer:

The length of one diagonal is 122 units.

Explanation:

Quadrilateral LMNO has diagonals that intersect at point P.

LMNO is a parallelogram.

P is intersection point of diagonals.

In parallelogram, diagonals are bisect each other.

Therefore, LP=NP because NL is a diagonal of parallelogram and P is mid point of NL.

6x - 5 = 4x + 17

6x - 4x = 17 + 5

2x = 22

x = 11

LN = 2(4x+17) Put x=11

LN = 2(4(11) + 17)

= 2(61)

= 122

Hence, The length of one diagonal is 122 units.

User Mesh
by
8.6k points
4 votes
LMNO is a parallelogram ⇒ LP=NP
6x-5=4x+17
2x=22
x=11
LP=6*11-5=61 cm
NP=4*11+17=61 cm
LP=PN=61 cm
LN=122 cm

User Tobin
by
7.9k points