Help! Geometry

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September 8th 2008, 10:40 AM
wynkky

Help! Geometry

The question is:

The oval athletic field is the union of a square and semicircles at opposites ends, as shown in Figure. If the area of the field is 1300 square yards, find the dimensions of the square.

Basically the figure is a football field with two semicircles at the end. I can do this problem forward, but going backward is not going so well.

Please help!

Kelli
September 8th 2008, 10:59 AM
Rinor Berisha

So you have a circle and a square. I think there has to be more info!
September 8th 2008, 11:23 AM
Shyam

Quote:

Originally Posted by wynkky

The question is:

The oval athletic field is the union of a square and semicircles at opposites ends, as shown in Figure. If the area of the field is 1300 square yards, find the dimensions of the square.

Basically the figure is a football field with two semicircles at the end. I can do this problem forward, but going backward is not going so well.

Please help!

Kelli

Let us suppose radius of the semicircular ends = r.

So, side of square = diameter of semicircle = 2r

Now area of field = Area of two semicircles + Area of square.

$1300 = 2 \times {\frac{\pi r^2}{2}} + (2r)^2$

$1300 = \pi r^2 + 4r^2$

$1300 = r^2(\pi + 4)$

$r^2 = \frac {1300}{\pi + 4}$

$r= \sqrt {182.032}$

r= 13.49 yards

Side of square = 2r = $2 \times 13.49$ = 26.98 yards.= 27 yards