Question

Kiran bent some wire around a rectangle to make a picture frame.the rectangle is 8 inches by 10 inches.1) find the perimeter of the wire picture frame2) if the wire picture frame was stretched out to make one complete circle, what would the radius be?

Answer 1

`\begin{gathered} 1.\text{ 62.8 inches} \\ 2.\text{ 10 inches} \end{gathered}`

Explanation:

Since the rectangle is 8 inches by 10 inches, the circles are:

1. Use the equation of the perimeter of a circle, the radio of the circle is 1 inch, therefore:

*There are 14 half circles (7 full circles) and 4 of the 3/4 circles.

`\begin{gathered} \text{ Total perimeter= }7\cdot(2\cdot\pi\cdot1)+4\cdot((3)/(4)\cdot(2\cdot\pi\cdot1)) \\ \text{ Total perimeter=}20\pi \\ \text{ Total perimeter=62.8 inches} \end{gathered}`

2. Now, for the radius of the wireframe if you stretched out the perimeter would be 62.8 inches, substitute for the perimeter and solve for the radius:

`\begin{gathered} 62.8=2\cdot\pi\cdot r \\ r=(62.8)/(2\pi) \\ r=10\text{ inches} \\ \text{ The radius would be 10 inches.} \end{gathered}`