Can someone please help me with these two questions:
1) A window is in the shape of an equilateral triangle on top of a rectangle so that the side length of the triangle is equal to the width of the rectangle. The frame of the window is 360cm in length (i.e. the window's perimeter is 360cm). Find the exact length of the triangle if the area of the window is the maximum possible.
2) Find the dimensions of the rectangle with the largest area which can be cut from a circle with the equation x^2+y^2=4
Both from MathsWork, q. 15 an 16 
Thanks!
1).
You know that the perimeter of the window is 360cm. From the shape of the triangle we can see that the perimeter will be given by:
(we exclude the other 'x' since it isn't a part of the perimeter).
From here we transpose to make 'y' the subject.
}{2})
Now we need to calculate the area of the window. We know we can do this easily since it is in two easy shapes (triangle and rectangle). The area of a rectangle is just the 2 sides multiplied together (xy):
}{2})
Next is the equilateral triangle and the general formula for the area of an equilateral triangle is common so we can simply use that to find the area of the triangle and add it to the area of the rectangle!
\cdot x+720)}{4})
If we know that the area is the maximum then we simply take the derivative and let it equal zero and solve for 'x'!
\cdot x}{2}+180)
\cdot x}{2}+180=0)
}{11})
I don't know what they mean by the exact length of the triangle (I presume the perimeter of the triangle??) if so then you can just times it by 3 to get your answer (since there are 3 sides) otherwise you can leave your answer like that I reckon (what 'x' equals).
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