Q30 of 47 Page 1

The perimeter of a right triangle is 60 cm. Its hypotenuse is 25 cm. Find the area of the triangle.

It is given in the question that,

Perimeter of right triangle = 60 cm


Also, Hypotenuse of right triangle = 25 cm


We know that, perimeter = a + b + c



∴a + b + c = 60


a + b + 25 = 60


a + b = 60 – 25


a + b = 35 (i)


Now, in triangle ACB by using Pythagoras theorem we have:


AC2 + BC2 = AB2


b2 + a2 = 625 (ii)


a + b = 35 [From (i)]


Now, by squaring both sides we get:


(a + b)2 = (35)2


a2 + b2 + 2ab = 1225


2ab = 1225 – 625 [From (ii)]


ab = 300 (iii)


Now, we know that area of triangle =





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