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

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

Grade:12

1 Answers

Rinkoo Gupta
askIITians Faculty 80 Points
6 years ago
let the base and perpendicular are x and y
then x2+y2=25
Area=xy/2

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


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