Question

A rectangle's perimeter and its area have the same numerical value. The length of the rectangle is 6 centimeters. Write an equation that can be used to find 's the width of the rectangle in centimeters.​

Answer 1

Let's denote the width of the rectangle as 'w' centimeters. The formula for the perimeter (P) of a rectangle is:

P = 2(length + width)

In this case, the length is given as 6 centimeters, so the equation for the perimeter is:

P = 2(6 + w)

Now, you mentioned that the rectangle's perimeter and area have the same numerical value. The formula for the area (A) of a rectangle is:

A = length × width

In this case, the length is 6 centimeters, so the equation for the area is:

A = 6w

Since you want the perimeter and area to have the same numerical value, you can set the two equations equal to each other:

2(6 + w) = 6w

Now, you can solve this equation for 'w' to find the width of the rectangle:

2(6 + w) = 6w

12 + 2w = 6w

12 = 6w - 2w

12 = 4w

Now, divide both sides by 4 to isolate 'w':

w = 12 / 4

w = 3

So, the width of the rectangle is 3 centimeters.