Question

In the parallelogram LMNO, if NM = x + 35 and OL = 5x + 3, find the value of x and then find the lengths of NM and OL.

a) x = 10, NM = 43, OL = 45
b) x = 8, NM = 45, OL = 43
c) x = 10, NM = 45, OL = 45
d) x = 8, NM = 43, OL = 43

Answer 1

To find x, solve the equation x + 35 = 5x + 3. Then substitute x into the expressions for NM and OL to find their lengths.

Step-by-step explanation:

To find the value of x, we can set NM equal to OL:

x + 35 = 5x + 3

Subtract x from both sides: 35 = 4x + 3

Subtract 3 from both sides: 32 = 4x

Divide both sides by 4: 8 = x

To find the lengths of NM and OL, we can substitute the value of x into the given expressions:

NM = 8 + 35 = 43

OL = 5(8) + 3 = 40 + 3 = 43