Question

The perimeter of a rectangle is 40 cm. Can it's area be 120 square centimetre. Why​

Answer 1

Answer:

The perimeter of a rectangle is twice its length plus twice its width. So 2L + 2W = 40 The area of a rectangle is its length times its width.

Answer 2

The perimeter of a rectangle is twice its length plus twice its width. So

2L + 2W = 40

The area of a rectangle is its length times its width. So

LW = 120 or

L = 120/W so

2 (120/W) + 2W = 40 or simplifying by dividing all terms by 2

120/W + W =20

Multiplying all terms by W gives you

120 + W^2 = 20W and by rearranging the terms

w^2 - 20W + 120 = 0 which can be solved using the quadratic formula

one of which parts is the square root of (b^2 - 4ac) which in this equation is

(20^2 - 4*120)^.5 or

(400 - 480) ^.5 or

(-80)^.5 which is an imaginary number and so

In real numbers, its area cannot be 120 sq cm.