Systems of Nonlinear Equations

[Lurid]

Homework Statement

A wire 60 feet long is cut into two pieces. Is it possible to bend one piece into the shape of a square and the other into the shape of a circle so that the total area enclosed by the two pieces is 100 square feet? If this is possible, find the length of the side of the square and radius of the circle.

Homework Equations

x+y=60, where x is one of the pieces cut, and y is the other.

(x/4)², which is the area of the square the one of the pieces make.

2∏R=y, which is the circle that the the piece y can make.
R=y/(2∏R)
∏R²=area of a circle
∏(y/(2∏R))²=
y²/(4∏)=

Two Equations:
x+y=100
(x/4)²+y²/(4∏)=100

The Attempt at a Solution

(x/4)²+y²/(4∏)=100
∏x²+4y² = (100)(∏)(16)

y=60/x

∏x²+4(60/x)² = (1600)(∏)
∏x⁴-1600∏x²+14400 = 0

I used the quadratic equation, solved for x and y. I plugged it back in and it didn't work out quite well. Is there anything wrong with my arithmetic or set-up? Or maybe it's impossible?

Any help is greatly, greatly appreciated!

 

[Steely Dan]

You have two mistakes, although one is typographical:

Two Equations:
x+y=100

This should be 60, according to the set-up.

y=60/x

According to the above equation, you should have $y = 60 - x$.

 

[Lurid]

You have two mistakes, although one is typographical:



This should be 60, according to the set-up.



According to the above equation, you should have $y = 60 - x$.

Thanks so much! I can't believe I couldn't catch that.
I still couldn't get a correct answer though (well, it doesn't work because x=74).

 

[Steely Dan]

Thanks so much! I can't believe I couldn't catch that.
I still couldn't get a correct answer though (well, it doesn't work because x=74).

It's a quadratic equation, so you should get two solutions. What's the other?

 

[Lurid]

It's a quadratic equation, so you should get two solutions. What's the other?

It was a negative number, -2.77. I'll just ask my teacher tomorrow. :)