Question

The difference between the length and width of a rectangle is 4 units. The perimeter is 40 units. Enter and solve a system of equations to determine the length and width of the rectangle. (Hint: The perimeter of a rectangle is 2l + 2w.)

Answer 1

Answer:the length and width of the rectangle are 12 and 8 respectively

Explanation:

Step 1

The perimeter of a rectangle is 2l + 2w where l= length and w= width giving us that

2l+2w=P

2l + 2w = 40

2(l+w)= 40

l +w = 20

Also we were given The difference between the length and width of a rectangle is 4 units giving us that

l-w= 4

Here our systems of equation to solve the problem

l-w= 4----- Equation 1

l +w = 20-----Equation 2

Step 2

I-w=4---- Equation 1

l +w = 20---Equation 2

Adding equation 1 and 2

I-w=4

+l +w = 20

2l =24

l=24/2

=l=12

To find w, we put the value of l=12 into equation 1

I-w=4

12-w= 4

w= 12-4

w=8

Therefore the length and width of the rectangle are 12 and 8 respectively