SOLUTION: The base of a traingle exceeds the height by 4 feet. If the area is 58.5 square feet, find the length of the base and the height of the triangle.

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Question 1069100: The base of a traingle exceeds the height by 4 feet. If the area is 58.5 square feet, find the length of the base and the height of the triangle.
Found 2 solutions by geo_freak, Boreal:
Answer by geo_freak(10) About Me  (Show Source):
You can put this solution on YOUR website!
Let's have the length of the height be "h".
The base exceeds the height (h) by 4 feet: h + 4
The area of the triangle is 58.5 square feet.
Area of triangle = (b x h) / 2
58.5 square feet = ((h + 4)(h))/2
Solve for h
%28%28h%2B4%29%28h%29%29%2F2+=+58.5+square+feet
%28h%5E2+%2B+4h%29+%2F+2+=+58.5
2%28%28h%5E2+%2B+4h%29+%2F+2%29+=+2%2858.5%29
2h%5E2+%2B+8h+=+117
2h%5E2+%2B+8h+-+117+=+0
h+=+5+sqrt%285%2F2%29+-+2
So base = 4+%2B+%285+sqrt%285%2F2%29+-+2%29 and height = 5+sqrt%285%2F2%29+-+2

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
height=x
base=x+4
(1/2)x(x+4)=58.5; A=(1/2)bh
x(x+4)=117
x^2+4x-117=0
(x+13)(x-9)=0
x=9 feet only positive root
base is 13 ft
height is 9 feet
Half their product is 58.5 sq ft.