Hello!
Given the formula for the area of a square is:
A=s2 where A is the Area and s is the length of the side of the square, we can find the length of one side of the square by substituting and solving:
9 in2=s2
√9 in2=√s2
3 in=s
s=3 in
Using the Pythagorean Theorem we can find the length of the squares diagonal which is also the diameter of the circle:
The Pythagorean Theorem states:
a2+b=c2 where a and b are legs of the triangle and c is the hypotenuse of the right triangle. In this case, both legs of the triangle are sides of the square so the are both the same length. Substituting and solving gives:
(3i n)2+(3i n)2=c2
9 in2+9 in2=c2
9 in2×2=c2
√9 in2×2=√c2
√9 in2√2 in=c
3 in√2=c
c=3√2 in
We can now find the perimeter of the square and the circumference of the circle.
Formula for Perimeter of a square is:
p=4s where s is the length of a side of the square.
Substituting and calculating p gives:
p=4×3 in
p=12 in
Formula for the circumference of a circle is:
c=2πr where r is the radius of the circle.
Or,
c=dπ where d is the diameter of the circle. Remember: d=2r
Substituting and calculating c gives:
c=3√2π in
We can then write the ratio of the circumference to perimeter as:
3√2π in12 in⇒
3√2π in124 in⇒
√2π4
