SOLUTION: A window has the shape of a rectangle with a right isosceles triangle on top. If the area of the window is to be 3m^2, what dimentions of the rectangle and triangle will minimize t

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: A window has the shape of a rectangle with a right isosceles triangle on top. If the area of the window is to be 3m^2, what dimentions of the rectangle and triangle will minimize t      Log On

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Question 1078694: A window has the shape of a rectangle with a right isosceles triangle on top. If the area of the window is to be 3m^2, what dimentions of the rectangle and triangle will minimize the perimeter of the window? Round answers to the nearest tenth of a metre.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x and y, dimensions of the rectangle;
base of the isosceles right triangle lies along x; the each leg of the isosceles triangle (the two congruent ones) is %28sqrt%282%29%2F2%29x.


AREA:
xy%2Bx%5E2%2F4=3

PERIMETER, p:
p=x%2Asqrt%282%29%2Bx%2B2y

p=x%2Asqrt%282%29%2Bx%2B6%2Fx-x%2F2
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dp%2Fdx=%28omittingSteps%29
dp%2Fdx=1%2F2%2Bsqrt%282%29-6%2Fx%5E2
dp%2Fdx=%28x%5E2%2Bsqrt%282%292%2Ax%5E2-12%29%2F%282x%5E2%29
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(Set derivative equal to 0 to solve for x dimension for the minimum perimeter p).
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This is not the completed solution.