Find the largest possible area of a right angled triangle whose hypotenuse is 5 cm long.
Given: Hypotenuse = 5 cm.
Let the two sides of right angle triangle be a and r.
According to the Pythagoras theorem, a2 + r2 = 25 …1
Assuming, area of triangle be, 
Condition for maxima and minima
= 0
= 0
r2 = 25 – r2
2r2 = 25
Since, r cannot be negative
Therefore, 
So, for 
,
Area will be maximum
From equation 1,
a2 + r2 = 25
10