SOLUTION: A 10‐foot piece of wire is cut into two pieces. One piece is bent to form a square. The other is bent to form a circle inscribed in the square. Approximately how long are the
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Question 252294: A 10‐foot piece of wire is cut into two pieces. One piece is bent to form a square. The other is bent to form a circle inscribed in the square. Approximately how long are the two pieces of wire?
a. 1.8 and 8.2 feet b. 2.4 and 7.6 feet c. 3.5 and 6.5 feet
d. 4.4 and 5.6 feet e. 4.9 and 5.1feet Found 2 solutions by ankor@dixie-net.com, palanisamy:Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A 10‐foot piece of wire is cut into two pieces.
One piece is bent to form a square.
The other is bent to form a circle inscribed in the square.
Approximately how long are the two pieces of wire?
:
let x = length of 1 piece, use this for the square
and
(10-x) = length of the other piece, for the circle
:
.25x = one side of the square
:
The side of the square will be the diameter of the circle
:
Find the circumference of the circle
c =
:
Circle + square = 10
() + x = 10
.7854x + x = 10
1.7854x = 10
x =
x = 5.6" is the one piece
and
10 - 5.6 = 4.4" is the other piece
:
I guess that would be (d), Merry Christmas!!
You can put this solution on YOUR website! Let a be the side of the square.
Since the circle is inscribed inside the square, the diameter of the circle is equal to the side of the square.
So, the diameter of the circle = a
Perimeter of the square = 4a
Perimeter of the circle = (22/7)a
Total length is 4a+(22/7)a = 10
(50/7)a = 10
a = (10x7)/50
a = 1.4
Perimeter of the square = 4a = 4x1.4 = 5.6 feet
Perimeter of the circle = 10-5.6 = 4.4 feet
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