UPSC CDS 2 2020 Math Paper

Assuming sides of right angled triangle as a,(a+2),(a+4)
As in triangle the biggest side is the hypotenuse for the right angled triangle
So by Pythagoras theorem - hypotenuse‌2 = base‌2 + hight‌2
(a+4)2=a2+(a+2)2
a2+16+8a=a2+a2+4+4a
a2−4a−12=0
(a−6)(a+2)=0
a=6
But a≠−2 as a cannot be negative.
Hence the sides are 6 , 8 and 10
So their product =6×8×10
= 480