Question 243174: The base of a triangle is 3cm greater than the height. The area is 14cm^(2). Find the height and length of the base.
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! Always start with the key formulas you know or are given in the setup. This step will reveal what the unknown is and should give you an idea of how to go about solving it. In this case we are told we are dealing with triangles.
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We know the area of a triangle is 1/2*base*height. We are told this is 14 sq. cm.
1/2*b*h =14
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We also are told the base is 3 cm > the height. We can express this in two ways:
b = h + 3
b - 3 = h
Either one of these will work when we substitute into the area formula to solve the problem.
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1/2 * b * h = 14
Multiply by 2 to remove the fraction
b * h = 28
Substitute for b
(h+3) * h = 28
h^2 + 3h = 28
Subtract 28 from both sides
h^2 + 3h - 28 = 0
Factor the equation. By inspection we see that the factors of 28 are 2*14 or 4*7. Since it is negative, we know the signs must be + and -. And the + needs to be 3 more than the -.
(h + 7)(h - 4) = 0
This means we have two proposed solutions to the problem: h = -7 & h = 4.
Since the height of triangle cannot be negative, we rule out -7.
Thus we are cautiously optimistic that: h=4.
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Recalling what we know from he setup,
b = h+3 = 4+3 = 7.
Now we we are optimistic that the base is 7, but we are not sure yet.
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To be sure, we have to check our work.
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What is the area of a triangle of base 7 and height 4?
1/2bh = 1/2(7)(4) = 14.
Yes.
So now we are confident. All that's left is to express the answer in exactly the language asked by the question. In this case:
The length of the base of the triangle is 7.
The height of the triangle is 4.
Done.
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