Kim is making rectangular greeting cards. Each card has an area of 12 square inches and the length is 1 inch more than the width. Find the length and width of her cards.

How about 3 by 4?

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To find the length and width of the greeting cards, we can set up an equation using the given information.

Let's assume that the width of the card is represented by the variable 'w'. Since the length is 1 inch more than the width, we can represent the length as 'w + 1'.

The area of a rectangle is given by the formula: Area = length x width.

Given that the area of the rectangular greeting card is 12 square inches, we can write the equation:

12 = (w + 1) x w

Simplifying the equation, we can distribute the w:

12 = w^2 + w

Rearranging the equation, we get a quadratic equation:

w^2 + w - 12 = 0

To solve this quadratic equation, we can factor it or use the quadratic formula. Let's use factoring:

(w + 4)(w - 3) = 0

Setting each factor equal to zero, we have two possible values for w:

w + 4 = 0 or w - 3 = 0

Solving these equations, we get:

w = -4 or w = 3

Since the width cannot be negative, we discard the value w = -4. Therefore, the width of the greeting card is 3 inches.

To find the length, we can substitute the width value (w = 3) into the expression for the length (w + 1):

Length = 3 + 1 = 4 inches

Therefore, the width of Kim's cards is 3 inches, and the length is 4 inches.