how many inches long is the radius of the largest circle that can fit inside a rectangle 18 inches long and 12 inches wide?
An 84-cm wire is cut into three pieces. the second piece is 4 cm longer than the first piece and the third piece is twice as long as the second piece. find the lenght of the shortest piece.
The circle diameter cannot be greater than 12 inches.
S-4=F
T=2S
T+S+F=84
2S+S+S-4=84 solve for Second (S).
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To find the length of the radius of the largest circle that can fit inside a rectangle, you need to determine the length of the shorter side of the rectangle.
Given that the rectangle is 18 inches long and 12 inches wide, the shorter side is 12 inches.
The radius of the largest circle that can fit inside the rectangle is equal to half the length of the shorter side.
So, the radius is 12/2 = 6 inches long.
Now, let's move on to the next question.
We are given that a 84-cm wire is cut into three pieces. Let's denote the lengths of the three pieces as a, b, and c, respectively.
According to the given information, b = a + 4 and c = 2b.
The sum of the lengths of the three pieces is 84 cm:
a + b + c = 84
Substituting the values of b and c, we get:
a + (a + 4) + 2(a + 4) = 84
Simplifying the equation:
a + a + 4 + 2a + 8 = 84
Combining like terms:
4a + 12 = 84
Subtracting 12 from both sides:
4a = 72
Dividing both sides by 4:
a = 18
So, the length of the first piece is 18 cm.
Now, to find the length of the shortest piece, we need to find the minimum value among a, b, and c.
Let's substitute the value of a back into the equations for b and c:
b = a + 4 = 18 + 4 = 22
c = 2b = 2(22) = 44
The shortest piece is the first piece, which has a length of 18 cm.
To find the length of the radius of the largest circle that can fit inside a rectangle, you can use the concept of the diagonal of the rectangle.
1. Start by drawing the rectangle with the given dimensions: 18 inches long and 12 inches wide.
2. The diameter of the circle will be equal to the smaller dimension of the rectangle, which in this case is 12 inches. The radius is half the diameter, so the radius of the circle is 12/2 = 6 inches.
Now, let's move on to the second question about the wire being cut into three pieces.
1. Let's assume the length of the first piece is x cm.
2. The second piece is 4 cm longer than the first piece, so its length can be expressed as (x + 4) cm.
3. The third piece is twice as long as the second piece, so its length can be expressed as 2 * (x + 4) cm.
4. The sum of the lengths of the three pieces is equal to the total length of the wire, which is 84 cm. So, you can form the equation: x + (x + 4) + 2 * (x + 4) = 84.
5. Simplify the equation: x + x + 4 + 2x + 8 = 84.
6. Combine like terms: 4x + 12 = 84.
7. Subtract 12 from both sides of the equation: 4x = 72.
8. Divide both sides of the equation by 4: x = 18.
Therefore, the length of the shortest piece is 18 cm.