Let the length of AB be xcm. ∴AC=(5x−4)cm and BC=(4x+4)cm Given, perimeter of △ABC=90 ⇒x+(5x−4)+(4x+4)=90 ⇒10x=90 ⇒x=
90
10
=9cm ∴AB=9cm,AC=5×9−4=41cm and BC=4×9+4=40cm Since, (41)2=(40)2+(9)2 [AC2=BC2+AB2] ∴△ABC is a right angle triangle with hypotenuse of 41cm. ∴ Area of △ABC=