the length of a rectangle is 2 inches longer than twice its width. If the area of the rectangle is 24 square inches, what are the dimensions?

The length is 8 inches and the width is 3 inches

Step-by-step explanation:

Let w represent the width.

The length can be represented by 2w + 2

Use the area formula, A = lw, and plug in the area and the expressions for the length and width:

A = lw

24 = (2w + 2)(w)

Simplify and solve for w:

24 = 2w² + 2w

2w² + 2w - 24

Divide everything by 2:

w² + w - 12

Factor:

(w + 4)(w - 3)

Set equal to 0 and solve for each factor:

w + 4 = 0

w = -4

w - 3 = 0

w = 3

Since the width cannot be negative, the width has to be 3.

Next, find the length by plugging in 3 as w:

2w + 2

2(3) + 2

= 8

So, the length is 8 inches and the width is 3 inches

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