SOLUTION: the height of a triangle is five feet less than two times the base. If the area is 75 square feet find the base and height.

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Question 106170: the height of a triangle is five feet less than two times the base. If the area is 75 square feet find the base and height.
Found 2 solutions by josmiceli, stanbon:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
A+=+75 sq ft
A+=+%281%2F2%29%2Ab%2Ah
Let the base = d
Let the height = h
h+=+2d+-+5
A+=+%281%2F2%29%2Ad%2A%282d-5%29
75+=+%281%2F2%29%2Ad%2A%282d-5%29
150+=+2d%5E2+-+5d
2d%5E2+-+5d+-+150+=+0
Use d+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
when equation is ax%5E2+%2B+bx+%2B+c+=+0
a = 2
b = -5
c = -150
d+=+%285+%2B-+sqrt%28+%28-5%29%5E2-4%2A2%2A%28-150%29+%29%29%2F%282%2A2%29+
d+=+%285+%2B-+sqrt%2825+%2B+1200%29%29+%2F+4
d+=+%285+%2B-+sqrt%281225%29%29+%2F+4
d+=+%285+%2B+35%29+%2F+4 (the negative sign makes no sense in this problem)
d+=+10 ft This is the base
h+=+2d+-+5
h+=+20+-+5
h+=+15 ft This is the height

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
the height of a triangle is five feet less than two times the base. If the area is 75 square feet find the base and height.
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Formula: Area = (1/2)(base)(height)
75 = (1/2)(x)(2x-5)
150 = x(2x-5)
2x^2-5x-150 = 0
(2x+15) (x-10)= 0
x=-15/2 ; x=10
Only x=10 is realistic (base = 10 ft.)
Then height = 2*10-5 = 15 ft.
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Cheers,
Stan H.