SOLUTION: Hi! May I get help with this problem? A wire 220 in. long is cut into two pieces. One piece is formed into a square and the other into a circle. If the two figures have the same

Question 120090: Hi! May I get help with this problem?
A wire 220 in. long is cut into two pieces. One piece is formed into a square and the other into a circle. If the two figures have the same area, what are the lengths of the two pieces of wire?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Let's say the wire is cut into two pieces, one of them is L inches, and the other is 220 - L inches.

If we take the first piece and form it into a square, each one of the sides of the square will be inches, so the area of the square will be

The area of a circle is given by , but since the circumference of a circle is given by we can say that the radius of a circle with circumference C is .

Now we can re-write the circle area formula as , then simplify to:

But we know that , so:

Multiply by

Take the square root

But we know that , so substitute:

Distribute and collect like terms:

Factor out L

And divide by

inches

, so

Simplify with LCD of

inches

Check your answer:

. So the areas are equal

Now add the two lengths:

, so the two lengths add to 220.

Answer checks.

Final note: the expressions for L and C developed above are the exact answers. If you want to use a calculator to develop a decimal approximation of the answer, remember that you should never express an answer based on calculations involving measurements to greater precision than the least precise measurement given. Since the length of the wire was expressed to the nearest inch, you should express your answer to the nearest inch as well.
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