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The height of a triangle is 5 centimeters longer than three times its base. Find the base of the triangle if its area is 6 square centimeters
Step 1. Area of Triangle =
where x=base, h=height and A=area of is one-half times base times height
(The height of a triangle is 5 centimeters longer than three times its base)
Step 3. Substitute height in Step 2 into equation in Step 1.
Step 4. Multiply 2 in both sides of last equation in Step 3 to get rid of denominator.
Simplify by subtracting 12 from both sides of equation yields
Step 5. The last equation of Step 4 is simply a quadratic equation. Then use the quadratic formula:
where a=3, b=5, and c=-12
|Solved by pluggable solver: SOLVE quadratic equation with variable|
|Quadratic equation (in our case ) has the following solutons:|
For these solutions to exist, the discriminant should not be a negative number.
First, we need to compute the discriminant : .
Discriminant d=169 is greater than zero. That means that there are two solutions: .
Quadratic expression can be factored:
Again, the answer is: 1.33333333333333, -3.
Here's your graph:
Step 6. Pick the positive number in the quadratic equation. In this case, we have the base x= 1.3333=4/3.
height is then
Area is then
square centimeters. This is the same answer to our given answer. So it check out.
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