A rope of length 84cm is made into a circle of which the area exceeds the area of a rectangle by 20 cm square. The length of the diagonal of the rectangle is 13cm. Find its area.

Answer 1

If the circle has radius r and the rectangle's dimensions are w and l, then
2πr = wl+20
w^2+l^2 = 13^2
2πr + 2(w+l) = 84

Solving these, we get

r = 5.843
w = 2.615
l = 12.734

wl = 32.300

Hmmm. With the diagonal a convenient 13, I had expected the rectangle to be 5x12, but not so.