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)
I know that the width is 6 and the length is 12, I just need to know the 2 equations that prove that this is true

Answer 1

Here are the two equations for this problem:

Let length = L

Let width = W

Equation No. 1 -

L = 2W

Equation No. 2 -

2L + 2W = 36

First simply substitute the value of ( L ) from the first equation into the second equation to solve for ( W ) as displayed below:

Equation No. 2 -

2L + 2W = 36

2 ( 2W ) + 2W = 36

4W + 2W = 36

6W = 36

W = 36 / 6

W = 6

Now, we substitute the value of ( W ) from the second equation into the first equation to solve for ( L ) as displayed below:

Equation No. 1 -

L = 2W

L = 2 ( 6 )

L = 12

Therefore, L = 2W and 2L + 2W = 36 are the correct equations for this problem.

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Answer 2

Answer:

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).