Question

The perimeter of a rectangular note card is 18 inches. The area is 18 square inches. What are the dimensions of the note card?

Answer 1

Answer: the length is 6 inches and the width is 3 inches.

Step-by-step explanation:

Let L represent the length of the rectangular note card.

Let W represent the width of the rectangular note card.

The formula for determining the area of a rectangle is expressed as

Area = L × W

Area of the note card would be

LW = 18 - - - - - - - - - - - - 1

The formula for determining the perimeter of a rectangle is expressed as

Perimeter = 2(L + W)

Perimeter of the note card would be

2(L + W) = 18

(L + W) = 9 - - - - - - - - - - - - 2

Substituting L = 9 - W into equation 1, it becomes

W(9 - W) = 18

9W - W² = 18

W² - 9W + 18 = 0

W² - 6W - 3W + 18 = 0

W(W - 6) - 3(W - 6) = 0

W - 6 = 0 or W - 3 = 0

W = 6 or W = 3

Substituting W = 3 into equation 1, it becomes

3L = 18

L = 18/3 = 6

Answer 2

Answer:

6 by 3

Step-by-step explanation:

a rectangle as 2 equal sides. so if we know that it is 6 by 3, then 6+6+3+3

=12+6=18

the area of a rectangle is base * height. so 6 * 3 = 18