SOLUTION: This is a geometry question, from my algebra class, we are working on quadatric equations. Iam so confused. I know the formula for area of a triangle. A = 1/2 b x h. But ca

Algebra ->  Algebra  -> Triangles -> SOLUTION: This is a geometry question, from my algebra class, we are working on quadatric equations. Iam so confused. I know the formula for area of a triangle. A = 1/2 b x h. But ca      Log On

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Question 21412: This is a geometry question, from my algebra class, we are working on quadatric equations. Iam so confused. I know the formula for area of a triangle. A = 1/2 b x h. But can't figure out how to come up with an equation to figure out how to do this.
The question:
The base of a triangle is 4 feet less than 3 times the height, and the area is 16 square feet. Find the dimensions of the triangle (Note: need to set up an equation to sove the problem) Please help!! Thank you.
Answer by josmiceli(6783) About Me  (Show Source):
You can put this solution on YOUR website!
let h = the height
let b = the base
let A = the area
A = 16 = (1/2)*b*h
multiply each side by 2
(a) 32 = b*h
from the description of the problem,
b = 3*h - 4
substitute this result for b into (a)
32+=+%283%2Ah+-+4%29%2Ah
32+=+3%2Ah%5E2+-4%2Ah
rearranging,
(b) 3%2Ah%5E2+-+4%2Ah+-+32+=+0
this is a quadratic equation
the roots (negative and positive) are given by
+%28-b+%2B-sqrt%28b%5E2+-+4%2Aa%2Ac%29%29%2F%282%2Aa%29
if the form of the equation is
a*h^2 + bh + c = 0
from our result in (b),
a = 3
b = -4
c = -32
%28-%28-4%29+%2B-+sqrt%2816+-+%284+%2A3%2A%28-32%29%29%29%29%2F%282%2A3%29
%284+%2B-+sqrt%2816+%2B+384%29%29%2F6+
%284+%2B-+sqrt%28400%29%29%2F6+
%284+%2B-+20%29%2F6+
choose the positive result
%284+%2B+20%29%2F6+
4+=+r1
therefore h = 4
32 = b*h
b = 32/4
b = 8
substitute these values back into
b = 3*h - 4
A = (1/2)*b*h