Question

The length of the rectangle is twice its width. Write and solve a system of linear equations to find the length L and width W of the rectangle (perimeter=36)

Answer 1

Hello from MrBillDoesMath!

Answer: L= 12, W = 6

Discussion:

Let "L' be the length of the rectangle,"w" its width, and P its perimeter. We are told that

L = 2W (*)

and

P = 36

Since the Perimeter of a rectangle = 2L + 2W we have

2L + 2W = 36

From (*) above L = 2W so substituting this into the last equation gives:

2L + L = 36

which gives 3L = 36 or L = 12. Since the Width is 1/2 the length, W = 12/2 = 6

Regards, MrB

Answer 2

The length is equal to 12 and the width is equal to 6.

Step-by-step explanation:

In order to find the values here, we start by setting the width equal to x. Now knowing this, we know that the length is twice that long. Therefore, the length would be equal to 2x. Now we can use the perimeter formula to solve the equation.

2L + 2W = P

2(2x) + 2(x) = P

4x + 2x = 36

6x = 36

x = 6

Now with the given value for x, we can tell that the width is 6 and then we multiply it by 2 to get the length value (12).