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

Explanation

From given, we have,

`x^2+y^2=5^2`

`Rightarrow y^2=25-x^2`

`therefore ysqrt(25-x^2)`

Let `A` be the area of the triangle

`therefore A=1/2 xy`

`Rightarrow A=1/2 x sqrt(25-x^2)`

`(d A)/(d x)=1/2[x d /(d x) sqrt(25-x^2)+sqrt(25-x^2)d/(dx) (x)]`.

...