SOLUTION: A right triangle has an area of 48cm^2 with one side that is twice as long as the other side. What is the hypotenuse of this triangle? The answer is 4 square foots 15. I kno

Algebra ->  Triangles -> SOLUTION: A right triangle has an area of 48cm^2 with one side that is twice as long as the other side. What is the hypotenuse of this triangle? The answer is 4 square foots 15. I kno      Log On


   

Question 787187: A right triangle has an area of 48cm^2 with one side that is twice as long as the other side. What is the hypotenuse of this triangle? The answer is 4 square foots 15.
I know these formulas: A=1/2 the base*height and the pythagoream therom
a^2 + b^2 = c^2.
I was trying to solve by doing the following: 48= 1/2b * 2b; the "2's" cancel.
48=b*b -----> 48=b^2. I can place the 48 into the pythagoream therom; however, I still have 2 variables and I do not know how to solve. a^2 + 48 = c^2.
Thank you for your help.
Shanell
Answer by Cromlix(4381) About Me  (Show Source):
You can put this solution on YOUR website!
Hi Shanell,
If you make one of the sides of your
triangle = x.
And the other 2x (Twice the length)
Area of a triangle = 1/2(base * height)
48 = 1/2 (x * 2x)
48 = x^2
x = sqrt%2848%29
So, one side of your triangle
would equal = sqrt%2848%29
And the other side = 2 * sqrt%2848%29
= sqrt%28192%29
As you said Pythagoras =
a^2 + b^2 = c^2
Squaring a square root leaves the number
So, 48 + 192 = c^2
c^2 = sqrt%28240%29
c = 4 square root 15.
Hope this helps.
:-)