Question

框架下部是边长分别为x,y的矩形,上部是斜边长为x的等腰直角三角形,要求围栏总面积为8

Answer 1

总面积=x^2/4+xy=8

y=8/x-x/4

用料=2x+2y+2*x*√2/2=2(√2+1)x+2y

=(2+√2)x+2(8/x-x/4)

=(√2+3/2)x+16/x

所以,

(√2+3/2)x=16/x

x^2=32/(√2+1)^2

x=4√2/(√2+1)=4√2(√2-1)=8-4√2

y=8/x-x/4=8/(8-4√2)-(8-4√2)/4

=2/(2-√2)-(2-√2)

=(2+√2)-(2-√2)

=2√2

即:

x=(8-4√2)米,y=2√2米 时用料最省