SOLUTION: The base of a triangle is 4 cm greater than the height. The area is 48cm^2. Find the height and base of the triangle.

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Question 1041162: The base of a triangle is 4 cm greater than the height. The area is 48cm^2. Find the height and base of the triangle.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
height = x
base = x+4

Area = 0.5*base*height
Area = 0.5*(x+4)*x
Area = 0.5x^2+2x

Plug in the given area of 48 and solve for x

Area = 0.5x^2+2x
48 = 0.5x^2+2x
0.5x^2+2x-48 = 0
x^2+4x-96 = 0
(x+12)(x-8) = 0
x+12 = 0 or x-8 = 0
x = -12 or x = 8

Ignore the negative solution
Since x = 8, this means x+4 = 8+4 = 12

Height= 8 cm
Base = 12 cm

Check:
0.5*base*height = 0.5*8*12 = 48
Answer is confirmed