A 120 ft fence will be cut into three pieces One piece will

A 120 ft fence will be cut into three pieces. One piece will be mode into o square, one piece will be made into an equilateral triangle and the third piece will be made into a rectangle where the length is twice the width. Find the length of each piece to minimize the area enclosed m the three fences.

Solution

Ans-

might start by drawing a line , and marking off 3 sections.
the second seems to be base, so set it equal to x
the first piece is twice as long, or 2x.
the third is three times as long or 3x.

Total length is 120, therefore
2x+x+3x=120
6x=120
x=20
returning to the sketch, we have 2x=40,,x=20,,,3x=60 (or longest)
check sum =120 ok