SOLUTION: The area of a triangle is 36 square meters. The height is two more than four times the base. Find the height and base. GOT THIS FAR: Let x = the base Let 4x + 2 = the heig

Algebra ->  Formulas -> SOLUTION: The area of a triangle is 36 square meters. The height is two more than four times the base. Find the height and base. GOT THIS FAR: Let x = the base Let 4x + 2 = the heig      Log On


   

Question 3170: The area of a triangle is 36 square meters. The height is two more than four times the base. Find the height and base.
GOT THIS FAR:
Let x = the base
Let 4x + 2 = the height
Let 36^ = area
x^2 + (4x+2)^2 = 36^2
Please help me. I am losing my mind.
Found 2 solutions by longjonsilver, cleomenius:
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
your base definition is a good start. Your height is correct. Now for the area:

area of triangle = %281%2F2%29bh

so, area = 36 = %281%2F2%29%28x%29%284x%2B2%29

72+=+4x%5E2+%2B+2x

so we get a quadratic, when we divide by 2 (to simplify a little): 2x%5E2+%2B+x+-+36+=+0

Hopefully this factorises nicely. If not - use the quadratic formula.

jon.

Answer by cleomenius(959) About Me  (Show Source):
You can put this solution on YOUR website!
The previous work is good:
36 = 1/2(4x + 2)*(x)
which evaluates to our quadratic
2x^2 + x -36 = 0
This does factor nicely
(2x + 9)(x - 4)
We take the positive 0; so x = 4.
36 = 1/2( (4 * 4 )+ 2) (4)
As we can see, this does check.