Question 21164
The area of a triange is 90 square feet.  The height is 2 less than twice the base.  Find the base and height of the triangle.
 

A={{{1/2}}}bh
A=90
h=2 less than twice the base 
so b=x 
and h=2x-2


Plug in what you know (I'll do it one by one)
A={{{1/2}}}bh
90={{{1/2}}}bh
90={{{1/2}}}(x)h
90={{{1/2}}}(x)(2x-2)
90=({{{1/2}}}){{{(2x^2-2x)}}}
90={{{(x^2-x)}}}


{{{(x^2-x-90)}}}=0
(x-10)(x+9)=0
x-10=0
x=10


x+9=0
x=-9



if x=10, H=2x-2, 2(10)-2=20-2=18,
h=18, b=10


if x=-9, h=2(-9)-2=-18-2=-20
h=-20, b=-9
but since we know that the height & base cannot have a negative value, "if x=-9" wouldn't work. 


the answer is h=18 and b=10