Find the largest possible area of a right angled triangle whose hypotenuse is 5cm long

A=[xv(25-x²)]/2

dA/dx=(1/2).[(25-2x²)/ v(25-x²)]

put dA/dx=0 ,then we get

x=5/v2

Now d²A/dx²=(1/2)[(2x³-75x)/(25-x²)^3/2]

Put x=5/v2, we get

D²A/dx²=-2 <0 so area is max at x=5/v2

So y²= 25-25/2=25/2

Y=5/v2

Thanks & Regards

Rinkoo Gupta

AskIITians Faculty