The perimeter of a right triangle =40cm
Hypotenuse measures =17cm.
Let x and y are the another sides.
40=17+x+y
x+y=23
or y=23−x
So, we have 3 sides as x,23−x and 17.
Apply Pythagoras theorem:
Hypotenuse2 = Base2+ Perpendicular2
172=x2+(23−x)2
289=x2+529+x2−46x
x2−23x+120=0
(x−8)(x−15)=0
x=8 or x=15
If x=8 then y=23−8=15
If x=15 then y=23−15=8
Now,
Area of triangle =12×base×height
=12×8×15
=60
Therefore, Area of triangle is 60cm2