SOLUTION: Find the value of x area of a triangle is 27 and the base is 4x+1 and the height is 3x

Algebra ->  Rectangles -> SOLUTION: Find the value of x area of a triangle is 27 and the base is 4x+1 and the height is 3x      Log On


   

Question 534867: Find the value of x
area of a triangle is 27 and the base is 4x+1 and the height is 3x
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Start with:
A+=+%281%2F2%29b%2Ah for the area of a triangle. Substitute A+=+27, b+=+4x%2B1, and h+=+3x
27+=+%281%2F2%29%284x%2B1%29%283x%29 Simplify.
27+=+%281%2F2%29%2812x%5E2%2B3x%29 Multiply both sides by 2.
54+=+12x%5E2%2B3x Subtract 54.
12x%5E2%2B3x-54+=+0 Factor 3 to simplify.
3%284x%5E2%2Bx-18%29+=+0 Factor the trinomial.
%284x%2B9%29%28x-2%29+=+0 Apply the zero product rule.
4x%2B9+=+0 or x-2+=+0 so...
4x+=+-9 and x+=+-9%2F4 or x+=+2 Discard the negative solution as this value of x (x+=+-9%2F4) would make the base and the height negative quantities.
x+=+2