Q10 of 137 Page 19

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




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