Answer
The answer is: 12 cm in length and 8 cm in width.
Work Step by Step
We assign the variables:
$l =$ length of the rectangle
$w=$ width of the rectangle
Step 1:
Find the equations that represent the problem.
The formula for the perimeter of a square is $P=2l+2w$. From the problem we know the perimeter is 40 cm.
$2l+2w=40$ -> Eq.1
We can get the second equation from the wording in the problem.
From " The length of a rectangle is 4 cm less than twice its width. ", we get
$l=2w-4$ -> Eq. 2
Step 2:
Solve the system of equations. Using the substitution method,
-> Substitute Eq. 2 into Eq. 1
$2(2w-4)+2w=40$
$4w-8+2w=40$
$6w=40+8$
$6w=48$
$w=\frac{48}{6}$
$w=8$
-> Substitute the value for $w$ into Eq. 2
$l=2(8)-4$
$l=16-4$
$l=12$
Step 3:
The answer is: 12 cm in length and 8 cm in width.
