Question

The perimeter of a rectangle is 24 inches. Find the dimensions if it’s length is 3 inches greater than its width

Answer 1

2l+2w=24
l=3+w
The first equation comes from the perimeter formula. Since it is a rectangle, there are two lengths and two widths, which must all be added to get the perimeter.  The second equation shows that the length is equal to the width plus three.  In order to solve this equation, the substitution method should be used, since the one equation is already set equal to one of the variables (L)

2l+2w=24
l=3+w

2(3+w)+2w=24
Use distributive property to get rid of the parentheses
2(3+w)+2w=24
2(3)+2(w)+2w=24
6+2w+2w=24
Simplify like terms on the left side of the equation
6+2w+2w=24
6+4w=24
Subtract six from each side so that all of the w's are on one side
6+4w-6=24-6
4w=18
Divide each side by four to find the value of one w
4w/4=18/4
w=4.5
Plug 4.5 into the one equation to find the value of l
l=3+4.5
l=7.5
Put the numbers into the first equation and simplify:
2(7.5)+2(4.5)=24
15+9=24
24=24
So the length would be 7.5 inches, and the width would be 4.5 inches