find the base and height of a triangle with area of 9 square ft if its base is 17 ft longer than its height?

Answer 1

the formula for area of trangle is (hxb)/2
since base is 17 ft longer than height, so,
b=17+h
area = (hxb)/2 = (hx(17+h))/2
9 = (h^2 + 17h)/2
-------------------- muliply by 2 both side
18 = h^2 + 17h
h^2 + 17 h -18 = 0
-------------------- get the factor!
(h+18)(h-1) = 0
so there are 2 possibility of h,
h=-18 or h=1, since h must be possitive,then h=1,
since b=17+h, b=17+1=18
so the base is 18 and height is 1.

Answer 2

Let x represent the height.
Then base will be x + 17.
Area of a triangle is 1/2 base times height.
So: (x + 17)/2 * x = 9
Solve for x:
(x^2 + 17x)/2 = 9
Multiply both sides by 2:
x^2 + 17x - 18 = 0
Factor into a binomial:
(x + 18)(x - 1) = 0
x = -18 or x = 1
Base is 18, Height is 1.