Question

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.

Answer 1

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?

Answer 2

im very lost after that point

Answer 3

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

Answer 4

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

Answer 5

okay i feel dumb after that. -8 and 10

Answer 6

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

Answer 7

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

Answer 8

thank you very much!