SOLUTION: The base of a triangle is five feet longer than the height. The area of the triangle is 75 square feet. Find the height and base of the triangle.

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Question 99: The base of a triangle is five feet longer than the height. The area of the triangle is 75 square feet. Find the height and base of the triangle.
Found 2 solutions by ichudov, bala:
Answer by ichudov(507) About Me  (Show Source):
You can put this solution on YOUR website!
base = height+5
The area is ++%28base%2Aheight%29%2F2++, so, base*height/2 = 75
since base = height + 5
(height+5)*height/2 = 75
(height+5)*height = 150
height%5E2+%2B5%2Aheight+=+150
height%5E2+%2B5%2Aheight+-+150+=+0
This is a quadratic equation, solve it using my solver.
I am including its graph: +graph%28+300%2C+300%2C+-18%2C+12%2C+-200%2C+200%2C+x%5E2%2B5x-150%29+
Looks like the only positive root is x=10.

Answer by bala(1) About Me  (Show Source):
You can put this solution on YOUR website!
Let the Height be x
so the base is x+5.
Area of a triangle = 1/2 (b*h).
Plugging in the values
1/2((x+5)*(x))=75.
multiplying by 2 on either sides, we get.
x2+5x=150.
solving the equation by completing the square method.
x2+5x =150
5*1/2=(5/2)2
gives us x2+5x+25/4=(150+25/4)2
(x+5/2)2 =sqroot of 625/4
giving us x+5/2 = 25/2
therefore x = -5/2(plus or minus)25/2
since we don't want a negative value. We take
-5/2+25/2. giving us 10 as the value for x, which is the height.
Plugging in the value for x as 10 in the 1st equation gives us the base as 15.