Answer:
To find the radius of a quarter circle based on the perimeter, you can use the formula for the perimeter of a quarter circle, which is:
[ P = \frac{1}{4} \times 2 \pi r + 2r ]
Here, ( P ) is the perimeter of the quarter circle, and ( r ) is the radius. This formula accounts for the curved part of the quarter circle (( \frac{1}{4} \times 2 \pi r )) and the two straight sides (each of length ( r )).
If you know the perimeter ( P ), you can solve for ( r ) by rearranging the formula:
[ r = \frac{P}{\pi + 2} ]
This will give you the radius of the quarter circle based on its perimeter. If you have a specific perimeter value, you can substitute it into the formula to calculate the radius.
