Recall that in a parallelogram, the diagonals bisect each other. That means they divide each other in exactly equal parts.
that means that if LW = 5 x + 2 , and LJ = 11 x + 2,
since LJ is the full diagonal segment, and LW is half of it, we can say:
LJ = 2 times LW
In mathematical terms:
LJ = 2 * (LW)
11 x + 2 = 2 * (5 x + 2)
use distributive property
11 x + 2 = 10 x + 4
subtract 10 x from both sides
11 x - 10 x + 2 = 4
x + 2 = 4
subtract 2 from both sides to isolate x completely on the left
x = 4 - 2
x = 2
Then now that we know the value of x, we can use it in the formula for LW:
LW = 5 x + 2 = 5 * 2 + 2 = 10 + 2 = 12
Then LW = 12
Then answer option A is the correct one.
