BTGmoderatorDC wrote:A circular patch is placed on a square piece of fabric. What is the perimeter of the square piece of fabric?
(1) The radius of the patch is 4 centimeters.
(2) Each side of the square piece of fabric is tangent to the patch.
OA C
Source: Princeton Review
Perimeter of the square= 4(length of each side)= \(4a\)
Notice the language: it does not say where the circle is place.. it just says on...
There are three cases
Case 1) the circle could meet the square at exactly at one point i.e the sides of the square becomes a tangent
Case 2) the circle could not touch the square at all. it could be at the center of the square.
case 3) the circle could touch at two points on each side
1) The radius of the patch is 4 centimeters.
If the circle is on the square we could find the perimeter, if not then no.
Not sufficient \(\Large{\color{red}\chi}\)
2) Each side of the square piece of fabric is tangent to the patch.
The measurement of any side is not given
Not sufficient \(\Large{\color{red}\chi}\)
Combining both 1 and 2
Only case 1 is possible \(\Large{\color{green}\checkmark}\)
Therefore, the correct answer is
C
