SOLUTION: The ratio for the diagonal and length of a rectangle is 8:5. Find the area of that rectangle it it is inscribed in a circle whose area is 120 sq. cm.

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Question 1013636: The ratio for the diagonal and length of a rectangle is 8:5. Find the area of that rectangle it it is inscribed in a circle whose area is 120 sq. cm.
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
If a rectangle is inscribed in a circle, then the diagonal of the rectangle is the diameter of the circle.
We can find the diameter from the area...
A = (pi)r^2 = (pi)(d^2/4) so that
120 = (3.14/4)(d^2) which leads to
d^2 = 152.87
d = 12.36 cm
Now the length is 5/8 of that or
(5/8)(12.36) = 7.73 cm
All we need is the width...we use Pythagoras for that
w^2 + 7.73^2 = 152.87 (which was d^2) so that
w = 9.65 cm (longer than the length?)
The area of the rectangle A = LW =
(7.73)(9.65) = 74.6 sq. cm.