MATh Geek plz!!?

Question

A wire 360 inches long is cut into 2 pieces. 1 piece is formed into a square adn the other into a circle. if the 2 figures have the same area, what are the lengths of the two pieces of wire.? to the nearest tenth of inch.

Answer 1

Let the respective pieces of wire be x inches and y inches
=>x+y=360
Now if a sqare is made by the x inch long wire,each of its side would be x/4 and the area would be x^2/16
if a circle is made of the second piece its circumference would be y inches or y=2XPiXr,where r is the radius of the circle or r=y/2Pi and its area would be PiXr^2=PiX(y/2Pi)(y/2PI)
=y^2/4Pi=y^2/12.57
Therefore by the problem x^2/16=y^2/12.57 =.x^2/y^2=16/12.57
=>x/y=4/3.545=1.128 =>x=1.128y
putting the value of x in the equation x+y=360,we get y=162.30 inches
therefore x=360-162.30=197.70
The pieces were 197.70 in and162.30 in

Answer 2

You need 2 equations.... First, set the formula for the area of a circle equal to the formula for the area of a square. The other thing you know is that the perimeter of the square plus the circumference of the circle equals 360. Since you have 2 equations and 2 unknowns, you should be able to solve the problem.

Let the side of the square = x and the radius of the circle = r.

Then A square = A circle, or (x)^2 = (pi)(r^2)

A square has 4 sides so perimeter = 4x and circumference of any circle = 2(pi)(r), thus 4x + 2(pi)(r) = 360

Now, using the 2nd equation, solve for x. Substitute x into the first equation and you can solve for r. You will have to do FOIL on the left side of the equation.

Once you have a number for r, plug it into either equation to get x.

Finally, use the numbers you determined for r & x, plug them into the formulae for perimeter and circumference, and you'll have the answer.

Answer 3

The lengths of wire are the perimeter of the shapes.

You need use substition equations for this problem.

Area of a square = l^2 (where l is the length of a side)
Perimeter of a square = 4 l
Area of a circle = pi r ^2 (where r is the radius from the centre to the outside)
and Circumference (perimeter) of a circle = 2 pi r

You know that the areas are the same so:
l^2 = pi r ^2

And you know that the perimeters add to 360 so:
4l + 2 pi r = 360

Solving the first equation in terms of l:
l^2 = pi r^2 ---- take the sq. rt. of each
l = rt pi r

Use this information in the second equation:
4l + 2 pi r = 360
4(rt pi r) + 2 pi r = 360 ---- I would substitute approx pi here to simplify
4 (1.77) r + 2 (3.14) r = 360

7.08 r + 6.28 r = 360
13.36 r = 360
r = 29.95 inches

If r = 29.95 inches you can go back 3 lines to substitute for the perimeters (lengths of wire) or:
Circumference = 2 pi r
= 59.9 pi
= approx. 188.2 inches

Perimeter of Sq. = 4 l (and you can substitute the horrible expression for l here) or
= Total length - Circle
= 360 - 188.2
= 171.8 inches

(l = 171.8/4 = 42.95 inches)

Double check using area formula

Answer 4

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Answer 5

not enough info.