HELPPP !! If O N = 8 x − 8 , L M = 7 x + 4 , N M = x − 5 , and O L = 3 y − 6 , find the values of x and y for which LMNO must be

Question

omeli [17]

2 years ago

12

HELPPP !! If O N = 8 x − 8 , L M = 7 x + 4 , N M = x − 5 , and O L = 3 y − 6 , find the values of x and y for which LMNO must be

a parallelogram

Mathematics

1 answer:

sveticcg [70] · Answer 1 · 2022-08-13T06:10:48+03:00

Answer:

x=12 and y=4.3

Step-by-step explanation:

Given the sides of quadrilateral that are O N = 8 x − 8 , L M = 7 x + 4 , N M = x − 5 , and O L = 3 y − 6. we have to find the value of x and y so that LMNO be a parallelogram.

we know opposite sides of parallelogram are equal.

Hence, we have to find the value of x and y such that opposite sides becomes equal which implies LMNO is a parallelogram.

Equating opposite sides equal, we get

8x-8=7x+4 ⇒ 8x-7x=8+4=12 ⇒ x=12

implies, NM=x-5=12-5=7

NM=OL ⇒ 3y-6=7 ⇒ 3y=13 ⇒ y=4.3

Hence, x=12 and y=4.3