# A 3 by 4 rectangle is inscribed in a circle. What is the circumference of the circle?

justaguide | College Teacher | (Level 2) Distinguished Educator

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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

giorgiana1976 | College Teacher | (Level 3) Valedictorian

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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` .