Question

the perimeter of a right angled triangle is 60 cm the hypothesis is 25 cm then find area of triangle

Answer 1

According to Pythagoras triplet.
The sides 15,20,25 form the sides of the right angled triangle.So the other 2 sides will be 15cm,20cm.So the base can be 15 or 20 it doesn't depend.
area of triangle =1/2*base*height
=1/2*15*20=150 cm2

Answer 2

The perimeter of right triangle = Base + height + hypotenuse
60 = b + h + 25
60 - 25 = b + h
35 = b + h ...... (1)
using pythagoras theorem
hypotenuse^2 = b^2 + h^2
(25)^2 = (b + h)^2 - 2bh [(a+b)^2 = a^2+b^2+2ab]
625 = 35^2 - 2bh [from equation (1)]
625 = 1225 - 2bh
2bh = 1225 - 625
2bh = 600
bh = 600/2 = 300 ...... (2)

area of triangle = 1/2 × b × h
area of triangle = 1/2 × 300 [from equation (2)]
Ans. area of triangle = 150 cm^2