SOLUTION: A wire, 130 cm long, is cut into two pieces. One piece is bent to form a square of side x cm and the other piece is bent to form a circle of radius r cm. The total area of the squa

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Question 999931: A wire, 130 cm long, is cut into two pieces. One piece is bent to form a square of side x cm and the other piece is bent to form a circle of radius r cm. The total area of the square and the circle is A cm^2.
(a) show that A= %28%28%28%26%23960%3B%2B4%29x%B2%29+-+%28260x%29+%2B+4225%29%2F+%26%23960%3B

if the formula plot doesn't work, this is the formula:
(((π+4)x²) - (260x) + 4225)/ π
(b) given that x and r can vary, find the value of x for which a has a stationary value
thanks in advance
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The contribution of length from the square is L%5B1%5D=4x.
The contribution of length from the circle is L%5B2%5D=2pi%2Ar
L%5B1%5D%2BL%5B2%5D=130
4x%2B2pi%2Ar=130
2x%2Bpi%2Ar=65
.
.
For the square,
A%5Bs%5D=x%5E2
For the circle,
A%5Bc%5D=pi%2Ar%5E2
So then,
A=A%5Bs%5D%2BA%5Bc%5D
A=x%5E2%2Bpi%2Ar%5E2
From the length above,
pi%2Ar=65-2x
r=%2865-2x%29%2Fpi
pi%5E2r%5E2=%2865-2x%29%5E2
pi%5E2r%5E2=4x%5E2-260x%2B4225
pi%2Ar%5E2=%284x%5E2-260x%2B4225%29%2Fpi
Substituting into the area formula,
A=x%5E2%2B%284x%5E2-260x%2B4225%29%2Fpi
A=%28pi%2Ax%5E2%29%2Fpi%2B%284x%5E2-260x%2B4225%29%2Fpi
A=%28%284%2Bpi%29x%5E2-260x%2B4225%29%2Fpi
.
.
.
Stationary value is where the derivative of A with respect to x equals zero.
2%284%2Bpi%29x-260=0
x=260%2F%282%284%2Bpi%29%29
x=130%2F%284%2Bpi%29