The area of a rectangular red sticker is 38 square millimeters. The perimeter is 42 millimeters. What are the dimensions of the sticker? millimeters by millimeters

Let's denote the length of the rectangle as L and the width as W.

From the problem, we know two things:

1. The area of the rectangle (Length x Width) is 38 square millimeters. So, L*W = 38.

2. The perimeter of the rectangle (2Length + 2Width) is 42 millimeters. So, 2L + 2W = 42.

We can simplify the second equation to L + W = 21 (by dividing the whole equation by 2).

Now we have a system of two equations, and we can solve it step by step:

1. Express W from the second equation: W = 21 - L.

2. Substitute W in the first equation: L*(21 - L) = 38.

3. Open the brackets: 21L - L^2 = 38.

4. Rearrange the terms: L^2 - 21L + 38 = 0.

This is a quadratic equation, and we can solve it using the quadratic formula: L = [21 ± sqrt((21)^2 - 4138)] / (2*1).

5. Calculate the discriminant: D = (21)^2 - 4138 = 441 - 152 = 289.

6. Since the discriminant is positive, there are two solutions: L1 = [21 + sqrt(289)] / 2 = 19, L2 = [21 - sqrt(289)] / 2 = 2.

7. Substitute L1 and L2 in the equation for W: W1 = 21 - L1 = 2, W2 = 21 - L2 = 19.

So, the dimensions of the sticker are 19 millimeters by 2 millimeters or 2 millimeters by 19 millimeters.