SOLUTION: A rectangular piece of stainless steel that is 24 inches wide is folded at the middle so as to form a gutter with a triangular cross-section that is 6x inches across the base. Exp

Algebra ->  Test -> SOLUTION: A rectangular piece of stainless steel that is 24 inches wide is folded at the middle so as to form a gutter with a triangular cross-section that is 6x inches across the base. Exp      Log On


   

Question 1058651: A rectangular piece of stainless steel that is 24 inches wide is folded at the middle so as to form a gutter with a triangular cross-section that is 6x inches across the base. Express the area of the cross section as a function of x, And find the domain.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A rectangular piece of stainless steel that is 24 inches wide is folded at the middle so as to form a gutter with a triangular cross-section that is 6x inches across the base.
Express the area of the cross section as a function of x,
:
Find the height (h) of the triangle using pythag, a^2 + b^2 = c^2 where
h = the hypotenuse (c)
a = 12
b = 3x
h = sqrt%2812%5E2+%2B+%283x%29%5E2%29
h = sqrt%28144+%2B+9x%5E2%29
find the area of the triangle; A = 1%2F2*b*h
A(x) = 1%2F2*6x%2Asqrt%28144-9x%5E2%29
cancel 2
A(x) = 3x%2Asqrt%28144-9x%5E2%29
:
And find the domain. x > 0; x < 4