The length of a rectangle is 3 inches more than twice its width, and its area is 65 square inches.

Question

 

What is the length and width?

 

Answer 1

The length of a rectangle is  3 inches more than twice its width

Let  the width of a rectangle  = x inches then

The length of a rectangle = (2x + 3) inches

Its area formula = length * width

Its area = (2x+ 3)*x

The area of a rectangle = 65 inches

There fore (2x + 3)* x = 65

2x^2 + 3x = 65

2x² + 3x - 65 = 0

2x² +13x - 10x - 65 = 0

2x² - 10x + 13x - 65 = 0

2x(x - 5) + 13(x - 5) = 0

Take out common term x - 5

(x - 5)(2x + 13) = 0

x - 5 = 0 and 2x + 13 = 0

x - 5 = 0

Add 5 to each side

Therefore x = 5

2x + 13 = 0

2x = -13

 x = -13 / 2

x is not a negitive

x = 5 inches

substitute x = 5 in the length = 2x + 3 and width = x

The length of a rectangle = 2(5) + 3 = 13inches

The width of a rectangle = 5 inches.