Let length of rectangle = lm and breadth = bm ⇒ Diagonal of rectangle, d=l2+b2 ⇒ Area = lb=120 -----(i) and Perimeter = 2(l+b)=46 ⇒ l+b=
46
2
=23 Squaring both sides, we get ⇒ (l+b)2=(23)2 ⇒l2+b2+2lb=529 ⇒ l2+b2+2(120)=529 [Using equation (i)] ⇒ l2+b2=529−240=289 Taking square root on both sides ⇒ l2+b2=√289=17 ∴ Leanth of diagonal = 17m