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.
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Your welcome. :)
Answer:
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