If ON = 8x - 8 LM = 7x + 4 NM = x - 5 and
OL = 3y - 6 find the values of x and y for
which LMNO must be a parallelogram
In a parallelogram, opposite sides are equal in length. Therefore, we need to equate the lengths of LM and NO, as well as ON and LM.
From the given information, we have:
LM = 7x + 4
NO = LM = 7x + 4
ON = 8x - 8 = LM = 7x + 4
Since LM = LM is true, we can equate the remaining sides:
7x + 4 = 8x - 8
Simplifying the equation, we have:
x = 12
Now, let's find the value of y for which OL = NO:
OL = NO
3y - 6 = 7x + 4
Substituting x = 12, we have:
3y - 6 = 7(12) + 4
3y - 6 = 84 + 4
3y - 6 = 88
Adding 6 to both sides, we get:
3y = 94
Finally, dividing by 3, we find:
y = 31
Therefore, in order for LMNO to be a parallelogram, x = 12 and y = 31.