Question

M letter B ABCD is a parallelogram

Answer 1

Answer:

a) w = 5

b) x = 5 or 6

Step-by-step explanation:

A)  The propety you want to use is that opposite sides of a parallelogram are equal.  In this case AB = DC and AD = BC

It then givs you the measure for AB and DC, so you know they are equal

w^2 - 5 = 4w

w^2 - 4w - 5 = 0

I am going to complete the square

(w - 2)^2 - 9 = 0

(w - 2)^2 = 9

w - 2 = +/- 3

w = +/-3 + 2

w = -1 or 5

Since length can't be negative we know w = 5.  It's not because w is negative mind you, but the side 4w is negative and w^2 - 5 would be negative.  if you could make w a negative number and still have 4w and w^2 - 5 be positive, that negative w would work

B)  here you want to use opposite angles are equal in a parallelogram.  So B = D and A = C

It gives us B and D so set them equal.

25 = x^2 - 11x + 55

x^2 - 11x + 30 = 0

(x - 11/2)^2 - 1/4 = 0

(x - 11/2)^2 = 1/4

x - 11/2 = +/-1/2

x = +/- 1/2 + 11/2

x = 5 or 6

Here both answers work.