Let the shorter sides be x and y, respectively, and x > y. By Pythagoras theorem: x2+y2=102....(1) Also, area of triangle:
1
2
xy=24⇒xy=48 Putting y=
48
x
in equation (1), we get: x2+(
48
x
)2=102 ⇒x4+2304=100x2 ⇒x4−100x2+2304=0 Let t=x2 ⇒t2−100t+2304=0 ⇒t=36,64 ∴x2=36 or 64 ⇒x=6 or 8 y=8 or 6 Since x > y, therefore, x = 8 cm and y = 6 cm When base is halved, we get new base of triangle = 16 cm When height is doubled, we get new height = 3 cm New hypotenuse =√162+32 =√265cm