The area of a rectangle is 112 cm sq. The base is 2 more than 2 times the height. What is the base length?

Answer 1

b = base
h = height

b = 2h + 2

Area = bh = (2h + 2)h = 112
2h^2 + 2h - 112 = 0
h^2 + h - 56 = 0
(h - 7)(h + 8) = 0

The height cannot be -8, so heoght = 7, base = 16, area = 112.

Answer 2

area = b * h = 112
b = 2 + 2*h
substituting the latter into the former, we get
(2 + 2h) * h = 112. Simplifying gives h^2 + h - 56, which
has solution from the quadratic formula
h = (-1 + sqrt(1 + 4*56) ) / 2 = 7
b = 16

Answer 3

b=2h+2
area = bh
112 = (2h+2)h
112 = 2h^2 +2h
h^2+ h -56=0
(h+8)(h-7) =0
so h =7 and b=16