A 3 by 4 rectangle is inscribed in a circle. What is the circumference of the circle?
The rectangle with sides 3 and 4 is inscribed in a circle. The four corners of the rectangle touch the circle. The diagonals of the rectangle are diameters of the circle.
As the length of the sides is 3 and 4, the length of the diagonal can be found by using the Pythagorean Theorem. It is equal to sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt 25 = 5
The circumference of a circle with radius r is given as 2*pi*r or pi*d where d is the diameter.
Here, the diameter is 5. The circumference is 5*pi.
The circumference of the circle is 5*pi
The length of rectangle is of 4 and the width is of 3. Since the rectangle is inscribed in a circle, then it's diagonal represents the diameter of the circle.
We'll recall the formula that gives the circumference of a circle:
C = 2*`pi` *r
The diagonal of the rectangle can be found using the Pythagorean theorem:
D^2 = 3^2 + 4^2
D^2 = 9 + 16
D^2 = 25 => D = 5
We could give the answer regarding the length of the diagonal, completing the missing place from the Pythagorean triple (3,4,5).
Since we know the diagonal, then we can calculate the circumference:
C = D`pi`
C = 5`pi`
Therefore, the circumference of the circumscribed circle is of 5`pi` .