Question

2. The length of a rectangle is 3 cm less than

twice its width. If the area of the rectangle is
20cm? then what are the dimensions?

Answer 1

4,5

Explanation:

Width = x

Length = 2x - 3

Area = 20

Length * width = 20

(2x - 3)* x = 20

2x *x - 3*x =20

2x² - 3x = 20

2x² - 3x - 20 = 0

2x² - 8x + 5x - 5*4 = 0

2x*(x - 4) + 5*(x - 4) = 0

(x - 4) (2x + 5) = 0

x- 4 = 0 {2x + 5 is ignored as length and width cannot be in negative}

x = 4

Width = 4

Length = 2x - 3 = 2*4 - 3 = 8 - 3 = 5

Answer 2

Answer: w = 4, l = 5

Explanation:

area of a rectangle = lw

l = 2w - 3 based on question

area = (2w-3)w multiply through parentheses

area = 2w^2 - 3w

area = 20 plug in area

20 = 2w^2 - 3w

move all terms to one side

2w^2 - 3w - 20 factor

(2w+5)(w-4) set both terms equal to 0 and solve

w = -2/5, 4

w can only be positive so w = 4

plug w into l

l = 2w - 3= = 2 * 4 - 3 = 5