SOLUTION: Find the dimensions of a right triangle if the area is 48 and one leg is 4 less than twice the other leg. my attempt goes this way: A=1/2 bh 48=1/2 (2x-4) (x) 48=1/2 (2x^2

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: Find the dimensions of a right triangle if the area is 48 and one leg is 4 less than twice the other leg. my attempt goes this way: A=1/2 bh 48=1/2 (2x-4) (x) 48=1/2 (2x^2      Log On

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Question 986511: Find the dimensions of a right triangle if the area is 48 and one leg is 4 less than twice the other leg.
my attempt goes this way:
A=1/2 bh
48=1/2 (2x-4) (x)
48=1/2 (2x^2-4x)
48=x^2-2x
0=x^2-2x-48
then i used quadratic formula but i'll only use plus sign here because i don't know how to type in the plus and minus sign.
----it seems i can't type the equation properly here--but i only substituted the formula from the equation i got in the area part.

here is my theory or the answer i got.
x=8
2x-4=12
i can't seem to get the hypotenuse using these two answers because i get a decimal answer.
c^2=a^2+b^2 , using the Pythagorean theorem, i got an answer with a decimal, which in my opinion is wrong.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
A=%281%2F2%29+bh........correct
48=%281%2F2+%29%282x-4%29%28x%29........correct
48=%281%2F2%29+%282x%5E2-4x%29........correct
48=x%5E2-2x........correct
0=x%5E2-2x-48........correct
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%2A1%2A%28-48%29+%29%29%2F%282%2A1%29+
x+=+%282+%2B-+sqrt%28+4%2B192+%29%29%2F2+
x+=+%282+%2B-+sqrt%28+196+%29%29%2F2+
x+=+%282+%2B-+14%29%2F2+
positive solution:
x+=+%282+%2B+14%29%2F2+
x+=16%2F2+
highlight%28x+=+8%29+=> this is a height
now find the length of the base
b=2x-4
b=2%2A8-4
b=16-4
highlight%28b=12%29=>the base
check:

A=%281%2F2%29+bh
A=%281%2F2%29+8%2A12
A=%281%2Fcross%282%291%29cross%28+8%294%2A12
A=4%2A12
A=48


the hypotenuse:
c%5E2=a%5E2%2Bb%5E2+
c%5E2=8%5E2%2B12%5E2+
c%5E2=64%2B144+
c%5E2=208+
c=sqrt%28208%29+
c=14.42220510185596+
highlight%28c=14.4%29+........must be decimal