The length of a rectangle is 2 cm less than its Width. What are the dimensions of the rectangle if it’s areas 80 cm²?

Answer 1

area = length (l) * width (w)

80 = l * w

Since l = w -2 , 80 = (w - 2) * w

Simplify: w² - 2w = 80

Solve by completing the square:

w² - 2w +1 = 80 + 1

(w - 1)² = 81

w - 1 = ± 9

w = 10

So the length is 8.

Answer 2

The dimensions can be represented by x and x - 2. When you multiply to find the area you have x^2 - 2x = 80. Subtract 80 from both sides and you have x62 - 2x - 80 = 0 The factors of 80 that differ by 2 are 8 and 10. Since the 2x is negative the factors to combine are -10 and positive 8.

You then set each equal to 0. x - 10 = 0 You then use the zero sum theorem to solve for x. x = 10

The dimensions are therefore 10 by 8.