Find the dimensions of the triangle that has an area of 30 square centimeters. It has a base of x cm., and a height of (x+17) cm.
The formula for the area is A = (1/2)bh, so we have 30 = (1/2)x (x+17).
Write this equation as x^2 + 17 x - 60 = 0. It has two solutions:
x = (-17 + sqrt{17^2 + 4*60})/2 = (-17 + sqrt{289 + 240})/2 = (-17 + sqrt{529})/2 = (-17 + 23)/2 = 6/2 = 3
and x = (-17 - sqrt{529})/2 = (-17 - 23)/2 = -40/2 = -20. The second solution makes no sense because the length is a non-negative number.
Answer: The base of the triangle is 3 cm and its height is 20 cm.
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