Question 161669: Have a right triangle with base h+7 and height of h. The area equals 60. What is the height? Answer by gonzo(654) (Show Source):
You can put this solution on YOUR website! height = h
base = h+7
area = 60
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formula for area = 1/2 base * height
base = h+7
height = h
area = 60
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formula becomes
(1/2)*h*(h+7) = 60
multiply both sides by 2 to remove the denominator.
h*(h+7) = 120
multiply out to remove parentheses
h^2 + 7*h = 120
subtract 120 from both sides of equation
h^2 + 7*h - 120 = 0
this is a quadratic equation with factors equal to
(h+15) * (h-8) = 0
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h = -15 no good because can't be negative.
answer is
h = 8
h+7 = 15
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1/2 base * height should = 60.
1/2 * (15) * (8) = 4 * 15 = 60.
answer is good.
h = 8.
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