The difference between the length and width of a rectangle is 2 units. the perimeter is 40 units. write and solve a system of equations to determine the length and width of the rectangle. (hint: the perimeter of a rectangle is 2l+2w.) and quickly

Length = 11 units and width = 9 units

Step-by-step explanation:

Let the length of rectangle be L and width of rectangle be w.

According to problem,

L - w = 2    {difference between the length and width of a rectangle is 2 units}

Perimeter, P = 2(L + w) = 2L + 2w

Since P = 40 (given)

So, 40 = 2L + 2w

or 20 = L + w

We got two equations as:

L- w = 2    (1)

And

L + w = 20     (2)

solving above two equations will give L and w.

Adding equation (1 ) and (2)

we get, L - w + L + w = 2 + 20

  2L = 22

L = 11

Then w = 20 - L = 20 - 11 = 9

Hence Length , L = 11 units

And width ,w = 9 units