SOLUTION: a square and a semicurcular region have the same perimeter. If the length of the radius of the semicirular region is 8 what is the length of a side of a square?

Question 223686: a square and a semicurcular region have the same perimeter. If the length of the radius of the semicirular region is 8 what is the length of a side of a square?
Found 2 solutions by tutor_paul, rapaljer:
Answer by tutor_paul(519) (Show Source): You can put this solution on YOUR website!
Perimeter of a semicircle is given by:

In this case, you are given r, so the perimeter of the semicircle (and the square) is:

The equation for the perimeter of a square (s=side of the square) is:

Since the perimeter of the square is the same as the circle, you can substitute the expression found for the perimeter of the circle into the equation for the perimeter of the square and solve for s:

====================
Good Luck,
tutor_paul@yahoo.com
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
If the radius of the semicircle is 8, then the circumference of the entire circle is .

Since it's a semicircle, take half of this, and add in a diameter of 16, and you get the perimeter of the semicircle is

Let x = side of the square, which has a perimeter of 4x.

Since the perimeter of the square equals the perimeter of the semicircle,

Divide both sides by 4:

R^2

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus

RELATED QUESTIONS
A square region with a side length of 2 inches lies within another, larger square region... (answered by lynnlo)
The length of a rectangular region is 20 meters less than four times its width. If the... (answered by drj,nerdybill)
if i have a square that has a shaded region that has a height of 120 and width of 180,... (answered by solver91311)
how do you find the perimeter of a shaded region of a circle the shaded region is 140 (answered by josgarithmetic,Edwin McCravy,josmiceli,AnlytcPhil)
A square is inscribed in a circle. If the length of the diagonal of the square is 6.4 cm, (answered by ankor@dixie-net.com)
A veterinarian wishes to use 132 feet of chain-link fencing to enclose a rectangular... (answered by jorel555)
how do you find the perimeter of a shaded region of a circle the shaded region is 140 (answered by Fombitz)
find the area of its region if the perimeter of a rectangle is 36... (answered by Theo)
if a rectangular region having an area of 500 square units has its length increased by 20 (answered by Fombitz)