Question 71280: This is another quadratic based question that I have in which I have NO idea how to format it. Please HELP!
Find the dimensions of a triangle whose area is 42 square centimeters and whose base and height together measure 19 centimeters.
I am sooo totally lost. I appreciate your help
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Find the dimensions of a triangle whose area is 42 square centimeters and whose base and height together measure 19 centimeters.
:
We know the area of a triangle: A = .5*b*h
Let x = the base
:
Remember it said,"base and height together measure 19 centimeters."
Therefore the height = (19-x);
:
.5*b*h = 42
.5*x*(19-x) = 42
:
Get rid of the fraction, mult equation by 2:
x(19-x) = 84
19x - x^2 = 84
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Arrange as a quadratic equation (subtract 84 from both sides):
-x^2 + 19x - 84 = 0
;
It easier to factor if the coefficient of x^2 is +1, mult eq by -1:
+x^2 - 19x + 84 = 0
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Factors to:
(x-7)(x-12) = 0
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x = 7 and x = 12; either is a good solution
:
If the base is 7, the height is 12
or
If the base is 12, the height is 7
:
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Check area using our solutions: .5*7*12 = 42
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Did this help you find your way?
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