Marker Buoy

Math need to solve a word problem -Functions?

A lifeguard uses 700 m of marker buoys rope off a rectangular swimming area in a lake. One side of the swimming area is sandy beach.
Determine the dimensions that will result in the maximum swimming area.

NO derivatives; solve without derivatives
the dimensions are 175 and 350; but i have no idea how to get the 175; I know how to get the 350

If the unknown width is w, then the length is 700 - 2w, and the area is w(700 - 2w). The function is

A = 700w - w^2

One root is at w=0, and the other root is a 700 - 2w = 0 ==> w=350.

This is a parabola, and parabolas are symmetrical. The maximum area occurs in the middle between the two roots, so w(max) is at (0 + 350) / 2 = 175 m.

If w = 175, then the length is 700 - 2 x 175 = 350 m, and the maximum area is 350 x 175 = 61, 250 sq. m.

Your dimensions are 350 by 175.

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