SOLUTION: please help me solve this problem. the area of a triangle is 13.5 meters. Find the base and height of the retangle if its height is 6 meters greaster than it's base. Use an eq

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the area of a triangle is 13.5 meters. Find the base and height of the retangle
if its height is 6 meters greaster than it's base. Use an equation and the formula area of a triangle =0.5(base)(height).

Found 2 solutions by nerdybill, gonzo:
You can put this solution on YOUR website!
the area of a triangle is 13.5 meters. Find the base and height of the retangle
if its height is 6 meters greater than it's base. Use an equation and the formula area of a triangle =0.5(base)(height).
.
Let b = length of the base
then because "its height is 6 meters greater than it's base"
b+6 = height
.
Plug the above into:
area of a triangle =0.5(base)(height)
13.6 =0.5(b)(b+6)
27.2 =(b)(b+6)
27.2 = b^2 + 6b
0 = b^2 + 6b - 27.2
.
Using the quadratic equation to solve we get:
b = {3.01664358259653, -9.01664358259653}
Throw out the neg solution.
b = 3 meters (base)
b+6 = 9 meters (height)
.
 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=144.8 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 3.01664358259653, -9.01664358259653. Here's your graph:

You can put this solution on YOUR website!
A = (b*h)/2 (equation 1)
where A = area
b = base
h = height
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h = b+6 (given)
A = 13.5 (given)
equation 1 becomes:
A = [b*(b+6)]/2 = 13.5
which becomes:
[b*(b+6)]/2 = 13.5 (equation 2)
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multiply both sides of equation 2 by 2:
b*(b+6) = 27
simplify:
b^2 + 6*b = 27
complete the squares:
(b+3)^2 = 27 + 9 (explanation for this down below after the answer)
simplify:
(b+3)^2 = 36
take square root of both sides:
b+3 = +/- 6
subtract 3 from both sides:
b = +/- 6 - 3
b becomes either:
6-3 = 3
or:
-6-3 = -9
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since b can't be negative, answer has to be:
b = 3
-----
since h = b+6, then:
h = 9
-----
you have:
b = 3
h = 9
A = 13.5 (given)
-----
substitute in equation 1:
A = (b*h)/2 (equation 1)
A = (3*9)/2 = 13.5
A = 27/2 = 13.5
A = 13.5 = 13.5
-----
values for b and h prove out.
equation is good.
b = 3
h = 9
-----
explanation for completing the squares is shown below:
also shown below is the fact that you could have also solved this using the quadratic formula.
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in order to complete the squares of your equation:
b^2 + 6*b)
i took half of the 6 and turned the equation into:
(b+3)^2
if you multiply this out, you will get:
b^2 + 6*b + 9
there's an extra 9 in there.
in order to keep the equations in balance i had to add 9 to the other side of the equation.
that's why the equation went from:
b^2 + 6*b = 27
to:
(b+3)^2 = 27 + 9
the additional 9 on the right hand side of the equation kept them in balance because i added 9 to the left hand side by completing the squares.
-----
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rather than completing the squares, you can also solve this equation using the quadratic formula.
the equation to solve was:
b^2 + 6*b = 27
subtract 27 from both sides of the equation:
b^2 + 6*b - 27 = 0
let x = b (this is necessary because general form of quadratic equation and quadratic formula use b for another purpose)
-----
formula becomes:
x^2 + 6*x - 27 = 0
general form of quadratic equation is:
a*x^2 + b*x + c = 0
general form of quadratic formula is: x =
a = 1
b = 6
c = -27
-----
b^2 = 36
4*a*c = -108
2*a = 2
-----