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

Question

Philoid · Accepted Answer

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

r² = 25 – r²

2r² = 25

Since, r cannot be negative

Therefore,

So, for ,

Area will be maximum

From equation 1,

a² + r² = 25