Respuesta :

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

Answer:

The length of one diagonal is 122 units.

Step-by-step 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.