Question 132322: The base of a triangle is 5cm greater than the height. The area is 18cm^2. Find the height and the lenghth of the base.
The height of the triangle is?
The base of the triangle is?
Answer by nycsharkman(136)   (Show Source):
You can put this solution on YOUR website! The base of a triangle is 5cm greater than the height. The area is 18cm^2. Find the height and the lenghth of the base.
The height of the triangle is?
The base of the triangle is?
We need the area of a triangle formula.
Here it is:
Area = (1/2) times base times height or A = (1/2)bh for short.
base = x + 5
area is 18
height = x
Plug this information into the formula and simplify.
A = (1/2)bh
18 = (1/2)(x + 5)x
18 = (x/2 + 5/2)x
18 = x^2/2 + 5x/2
Multiply both sides of the fractional equation by the LCD which is 2.
This is done to remove the fractions.
18(2) = 36
x^2/2 times 2 = x^2
5x/2 times 2 = 5x
We now have this equation:
36 = x^2 + 5x
Subtract 36 from both sides and equate everything to zero.
x^2 + 5x - 36 = 0
We now have a quadratic equation. Do you agree?
Factor the left side, if possible.
x^2 + 5x - 36 becomes (x + 9)(x - 4)
We now set each factor to zero and solve for x.
x + 9 = 0
x = -9...REJECTED!!
=========
x - 4 = 0
x = 4...ACCEPTED!!
Since we are dealing with length, the answer x = -9 is rejected because distance CANNOT be negative.
As given above, base = x + 5.
We just found that x = 4.
base = 4 + 5 = 9
height = x = 4
base = 9cm and height = 4cm
Is this clear to you?
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