a circle enclose a rectangle of side 6cm and 8cm. what is the perimeter of the circle?
Draw perpendicular lines through the middle of the rectangle. Also draw a line from the center of the circle a corner of the rectangle. Notice the 3-4-5 triangle, with 5 cm being the radius of the triangle.
The circle perimeter is 10 pi
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To find the perimeter of a circle, we need to know its radius. Since you have given the dimensions of a rectangle, we can use that information to determine the radius.
First, let's consider the rectangle that is enclosed by the circle. We know the sides of the rectangle are 6 cm and 8 cm. Since the circle encloses the rectangle, the diameter of the circle will be equal to the diagonal of the rectangle.
Using the Pythagorean theorem, we can find the diagonal (d) of the rectangle:
d^2 = 6^2 + 8^2
d^2 = 36 + 64
d^2 = 100
d = √100
d = 10 cm
Since we know the diameter (d) of the circle, the radius (r) can be calculated by dividing the diameter by 2:
r = d/2
r = 10/2
r = 5 cm
Now that we have the radius, we can find the perimeter (P) of the circle using the formula:
P = 2πr, where π (pi) is a constant approximately equal to 3.14159.
P = 2π(5)
P = 10π
Therefore, the perimeter of the circle is 10π cm or approximately 31.42 cm (rounded to two decimal places).