Question 319348
The base of a triangle is 4 inches less than twice the height.
 The area is 35 inches^2. Find the height and the base.
:
Let x = the height
then
(2x-4) = the base
:
The area: {{{1/2}}b*h = 35
Substitute for b and h
{{{1/2}}}*(2x-4)*x = 35
Multiply both sides by 2, get rid of the fraction
 2x^2 - 4x = 2(35)
Arrange as a quadratic equation:
2x^2 - 4x - 70 = 0
simplify, divide by 2
x^2 - 2x - 35 = 0
Factors to
(x-7)(x+5) = 0
The positive solution
x = 7 in is the height 
then
2(7) - 4 = 10 in is the base
:
:
Check the area with these values
.5 * 7 * 10 = 35