# Math Help - Another word problem!

1. ## Another word problem!

A circle and a square have the same area. Find the length of the diagonal of the square divided by the radius of the circle. (Hint: draw a diagram and label unknowns.)

2. Originally Posted by lilikoipssn
A circle and a square have the same area. Find the length of the diagonal of the square divided by the radius of the circle. (Hint: draw a diagram and label unknowns.)

Since they have the same area we know.

$A=\pi r^2 \mbox{ and } A=s^2 \iff \pi r^2=s^2 \iff r^2=\frac{s^2}{\pi}$

$r=\frac{s\sqrt{2}}{\sqrt{\pi}}$

Now using the pythagorean theorem we know the length of the diagonal is

$d^2=s^2+s^2 \iff d^2 =2s^2 \iff d=s\sqrt{2}$

Now we are asked to find the ratio of diagonal to the radius

$\frac{s\sqrt{2}}{\frac{s\sqrt{2}}{\sqrt{\pi}}}=\sq rt{\pi}$