Question

Samantha’s rectangular gift is 10 inches. by 12 inches and is framed with a ribbon. She wants to use the same length of ribbon to frame a circular clock. What is the maximum radius of the circular clock? Round to the nearest whole number.
(JUSTIFY)

Answer 1

Answer:

The maximum radius of the circular clock is 7 in

Step-by-step explanation:

We must calculate the perimeter of the rectangle

We know that the rectangle is 10 in x 12 in

If we call L the rectangle length and we call W the width of the rectangle then the perimeter P is:

$P = 2L + 2W$

Where

$L = 10$

$W = 12$

$P = 2 * 10 + 2 * 12\\\\P = 20 + 24$

$P = 44\ in$

Now we know that the perimeter of a circle is:

$P = 2\pi r$

In order for the perimeter of the circumference to be equal to that of the rectangle, it must be fulfilled that:

$2\pi r = 44\\\\r=\frac{44}{2\pi}\\\\r=7\ in$

We solve the equation for r

Answer 2

Answer:

7 inches

Step-by-step explanation:

The dimension of the rectangular gift is 10 by 12 inches so let us find the perimeter of this rectangle.

Perimeter of rectangular gift = 2 (L+ W) = 2 (10 +12) = 44 inches

Since we are to use the same length of ribbon to wrap a circular clock so the perimeter or circumference should be 44 inches.

$2\pi r=44$

$r=\frac{44}{2\pi }$

$r=7.003$

Therefore, the maximum radius of the circular clock would be 7 inches.