Question

The area of a rectangle is 20. The length is 3 less than twice the width. Find the length and the width

Answer 1

The length of rectangle is 5 units and width is 4 units.

Step-by-step explanation:

Given,

Area of rectangle = 20

Width of rectangle = w

Length of rectangle = 2w-3

Area = Length * Width

$20=(2w-3)(w)\\20=2w^2-3w\\2w^2-3w-20=0$

Factorizing

$2w^2-8w+5w-20=0\\2w(w-4)+5(w-4)=0\\(2w+5)(w-4)=0$

Either;

2w+5=0         =>2w=-5

Or,

w-4 = 0           => w=4

As width cannot be negative, therefore,

width of rectangle = 4 units

length of rectangle = 2w-3 = 2(4)-3 = 8-3 = 5 units

The length of rectangle is 5 units and width is 4 units.

Keywords: area, rectangle

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