the hypotenuse of the right angled triangle is 6cm more than twice the shortest side. if the third side is 2 cm less than the hypotenuse. find the 3 sides

Let the base be p

Hypotenuse = 2p + 6

Perpendicular = 2p + 4

By Pythagoras theoram

(2p+6) ^2 = (2p+4) ^2 + p^2

=> 4p^2 + 36 + 24p = 4p^2 + 16 + 16p + p^2

=> 36 + 24p = p^2 + 16p + 16

=> p^2 - 8p - 20 = 0

=> p^2 - 10p + 2p - 20 = 0

=> p (p-10) + 2 (p-10) = 0

=> (p-10) (p+2) = 0

p = 10 and - 2

Length can't be negative

So,

p = 10

Base = 10

Perpendicular = 24

Hypotenuse = 26