if the triangle has side b, and the circle has circumference c, then
2b+b√2 + c = 27
so, b = (27-c)/(2+√2)
the area is
a = 1/2 b^2 + πr^2
= 1/2 ((27-c)/(2+√2))^2 + π(c/(2π))^2
This a parabola with vertex (minimum area) at
c = 27(1 - 1/(1+(3-2√2)π)) = 9.45
27 ft of wire is to be used to form an isosceles right triangle and a circle. Determine how much of the wire should be used for the circle if the total area enclosed is to be a minimum? Maximum?
1 answer