SOLUTION: 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

Question 212048This question is from textbook
: 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 This question is from textbook

Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
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

Step 2. (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 centimeters
Area is then square centimeters. This is the same answer to our given answer. So it check out.

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