SOLUTION: The height of a triangle is 2 units more than its base. If the base is increased by 4 units and the height is decreased by 2 units, the area of the resulting triangle will be 8 sq

Question 675298: The height of a triangle is 2 units more than its base. If the base is increased by 4 units and the height is decreased by 2 units, the area of the resulting triangle will be 8 square units more than the area of the original triangle. Find the base and the height of the original triangle.
I've just learned that this is a quadratic equation and that the formula is A = 1/2bh. Area equals one half the base times height.
So, I think its supposed to be 1/2 (x + 4)(x + 2) - 2 = 8. I'm obviously doing something wrong because the instructors answer is that the base is 8 and the height is 10. What did I not do correctly?
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
The height of a triangle is 2 units more than its base. If the base is increased by 4 units and the height is decreased by 2 units, the area of the resulting triangle will be 8 square units more than the area of the original triangle. Find the base and the height of the original triangle.
**
original triangle:
let x=base
x+2=height
Area=(1/2)(x)(x+2)
..
2nd triangle:
x+4=base
(x+2)-2=x=height
Area=(1/2)(x+4)(x)
..
area of 2nd triangle-area of original triangle=8
(1/2)(x+4)(x)-(1/2)(x)(x+2)=8
LCD:2
x(x+4)-x(x+2)=16
x^2+4x-x^2-2x=16
2x=16
x=8
x+2=10
..
base of original triangle=8 units
height of original triangle=10 units

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