SOLUTION: 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. Please help me with this problem. Thank you.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 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. Please help me with this problem. Thank you.      Log On


   

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. Please help me with this problem. Thank you.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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%2F2%7D%7Db%2Ah+=+35%0D%0ASubstitute+for+b+and+h%0D%0A%7B%7B%7B1%2F2*(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