Question

如图,直角△ABC中,∠C=90度,AB=二倍根号五,sinB=五分之根号五,点P为边BC上一动点,PD‖AB,PD交A

Answer 1

(1)AB=2√5,sinB=√5/5=AC/AB

AC=ABsinB=2√5*(√5/5)=2

BC^2=AB^2-AC^2=20-4=16

BC=4

(2)△ABC与△DPC相似,PC:BC=DC:AC

PC*AC=BC*DC

2x=4DC

x=2DC

△ADP的面积为Y=PC*AD/2=x(AC-DC)/2=x(2-DC)/2

2Y=x(2-DC)

4Y=x(4-2DC)=x(4-x)

Y=x-x^2/4=-(1-x/2)^2+1

当x=2时,Y最大=1