If ON = 8x - 8, LM = 7x + 4, NM = x - 5, and OL = 3y - 6, find the values of x and y such that LMNO is a parallelogram.
Mathematics · Middle School · Thu Feb 04 2021
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To find the values of x and y such that LMNO is a parallelogram, we need to use the properties of parallelograms. One key property of a parallelogram is that opposite sides are equal in length.
Given: - ON = 8x - 8 - LM = 7x + 4 - NM = x - 5 - OL = 3y - 6
LMNO is a parallelogram, so LM = ON (opposite sides are equal), and OL = NM (opposite sides are equal as well).
From LM = ON: 7x + 4 = 8x - 8
Solving for x: 7x - 8x = -8 - 4 -x = -12 x = 12
Now we know that x = 12, let's find y using OL = NM:
OL = 3y - 6 NM = x - 5 Since x = 12, substitute x in NM: NM = 12 - 5 = 7
Now we have: 3y - 6 = 7
Solving for y: 3y = 7 + 6 3y = 13 y = 13/3
Therefore, the values of x and y are x = 12 and y = 13/3.