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### Best Answer I'M BANNED Y'ALL!!!!!!!!!! says

Okay, 2x + 2y = 28 and xy = 48, which means the dimensions of the rectangle are x = 8 and y = 6. I used guess and check to get the answer since I assumed you would make it something easy.

A rectangle with sides 8 and 6 has a diagonal of 10, and what do you know, the diagonal of the rectangle is the diameter of the circle. Whoa dood, I just blew your mind.

Since the diameter is 10, the radius is 5, and the area of the circle is 25*pi or about 78.54.

We posted at the same time!

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### CWanamaker says

Since the center of the circle and the rectangle coincide, the radius of the circle must be equal to half of the diagonal of the rectangle.

With that said we must solve for the diagonal length first.

Since A = LW = 48 and P = 28 = 2(L+W) we have a system of equations:

0 = LW - 48 and

0 = 2L + 2W - 28

Therefore W = 6 and L = 8

Now the Pythagorean theorem to solve for the total length of the diagonal: H = 10.

Since half the diagonal equals the radius, r = 5

Therefore the area of the circle is (pi)r^2 = (3.14)(5)(5) = 78.54.

Thank you, nice work! Tussin's answer was posted first just by a hair.