Let the length and breadth of the rectangular sheet be x mand ym respectively
Given, 2(x+y)=42 and x+y=21 . . . (i) x×y=108 y=
108
x
⇒y=
108
x
Put this value in Eq. (i), x+
108
x
=21 ⇒x2−21x+108=0 ⇒x2−12x−9x+108=0 ⇒x(x−12)−9(x−12)=0 ∴x=9 and 12 and y=12, and 9[∵ from Eq. (i)] ∴ Length of the diagonal BD=√(DC)2+(BC)2 =√(12)2+(9)2=√144+81 =√225=15m