the base of a triangle with an area of 40 m^2 is 2 meters longer than its height. find the base of the triangle.

Question

anonymous · Answer

Set up an equation using the formula for the area of a triangle.
$$A = \frac{1}{2}bh$$$$40 = \frac{1}{2}(x + 2)(x)$$$$80 = x(x + 2)$$$$80 = x^{2} + 2x$$$$0 = x^{2} + 2x - 80$$Can you solve the quadratic?

anonymous · Answer

im very lost after that point

anonymous · Answer

Alright. What you do here is find factors of -80 that can add up to 2. Tell me what you get.

anonymous · Answer

10 and 8? that doesnt really make sense cuz only 1+1 is 2..

anonymous · Answer

okay i feel dumb after that. -8 and 10

anonymous · Answer

then it would be (x-8)(x+10) right?

anonymous · Answer

Alright, factor it using those:
(x - 8)(x + 10) = 0
THen solve for x.
x = 8, -10
However, distances can't be negative, so the length of the height is 8. THe base is 2 more. b = 10

anonymous · Answer

thank you very much!