For a contest, students have to solve this problem: The length of a rectangle is 6 cm more than its width. The perimeter of the rectangle is 84 cm. What are the dimensions of the rectangle?

a) One student says the dimensions of the rectangle are 39 cm by 45 cm. Is the student correct? How do you know?

b) What is the answer to the contest problem?

The rectangle is definitely not 39 by 45 because those two numbers alone = the perimeter. As for the rectangle call the length (x+6) and the width x. Then say that 84=2(x)+2(x+6). solve for x

a) To determine if the student is correct, we can use a systematic approach to solve the problem.

Let's assume the width of the rectangle is x cm. Since the length is 6 cm more than the width, the length would be x + 6 cm.

The formula for the perimeter of a rectangle is 2(width + length). Substituting the given values, we have:

2(x + x + 6) = 84

Simplifying the equation gives us:

2(2x + 6) = 84
4x + 12 = 84
4x = 72
x = 18

Therefore, the width of the rectangle is 18 cm.

Now, substituting this value back into the equation for the length, we have:

Length = Width + 6
Length = 18 + 6
Length = 24 cm

So, according to our calculations, the dimensions of the rectangle are 18 cm by 24 cm.

Comparing these results to what the student suggested (39 cm by 45 cm), we can conclude that the student's answer is incorrect.

b) The dimensions of the rectangle are 18 cm by 24 cm.