UPSC 2014 CDS I Math Paper

Let n,n+1 and n+2 be the three consecutive sides of a right-angled triangle.
(n+2)2=(n+1)2+n2
⇒n2+4n+4=2n2+2n+1
⇒n2−2n−3=0
⇒(n−3)(n+1)=0
⇒n=3,−1
But, n cannot be negative. So, n = 3.
Thus, the sides of the triangle are 3 cm, 4 cm and 5 cm.
Area of the triangle =

1

2

×3×4=6cm2