A piece of cardboard in the shape of a parallelogram is twisted to form the tube for a roll of paper towels. The parallelogram has an area of 60 square inches. If its height h is 7 inches more than the length of the base b, what is the length of the base? (Hint: The formula for the area of a parallelogram is A = bh in

base = 5 in

height = 12 in

Step-by-step explanation:

Area = base x height

Base = b

Height = b+7

So:

60 = b (b+7)

60 = b^2 + 7b

0 = b^2 + 7b - 60

Applying quadratic formula:

a = 1; b=7; c=-60

For: ax2 + bx + c

x = [ - b ± √b²-4ac] / 2a

Replacing with the values given:

x = [ - 7 ± √ (7) ²-4 (1) - 60] / 2 (1)

x = [ - 7 ± √49 + 240] / 2

x = [ - 7 ± √289] / 2

x = [ - 7 ± 17] / 2

Positive:

x = [ - 7 + 17] / 2 = 5

So:

b = 5 in (base)

Height = b+7 = 5+7 = 12 in

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