Let length of one diagonal is a unit and length of another diagonal is b unit. It is given that diagonals of a rhombus differ by 2 units ⇒ a=b+2 Perimeter of the rhombus =2√a2+b2 According to question ⇒2√a2+b2−(a+b)=6 ⇒2√(b+2)2+b2−(b+2+b)=6 ⇒2√2b2+4+4b=2b+8 ⇒4(2b2+4b+4)=4b2+64+32b ⇒4b2−16b−48=0 ⇒b2−4b−12=0 ⇒b2−6b+2b−12=0 ⇒b(b−6)+2(b−6)=0 ⇒(b−6)(b+2)=0 ⇒b=6 or b=−2 Length of diagonal can not be negative. Hence, Length of diagonal is 6 cm Also, a = b +2 = 6 + 2 = 8 units Hence, Area of rhombus =