A rectangular price tag has an area of 36 square centimeters. Its perimeter is 26 centimeters. What are the dimensions of the price tag?

4 cm by 9 cm

Step-by-step explanation:

The formula for area of a rectangle is A = LW, where L and W are the dimensions of the rectangle. We have

36 = LW

The formula for perimeter of a rectangle is P = 2L + 2W. We have

26 = 2L + 2W

Solve the area formula for any variable ...

36/L = W

Plug that into the perimeter equation ...

26 = 2L + 2 (36/L)

Now simplify ...

26 = 2L + 72/L

Multiply all 3 terms by L to get rid of the fraction ...

26L = 2L² + 72

Now this is a quadratic equation, get all terms to one side and solve ...

2L² - 26L + 72 = 0

Divide both sides by 2

L² - 13L + 36 = 0

Factor the left side

(L - 9) (L - 4) = 0

So L = 4, or 9

If L = 4, then W = 36/4 = 9

If L = 9. then W = 36/9 = 4

either way, the dimensions are 4 cm by 9 cm