SOLUTION: The length of a rectangle is 6 cm longer than its width. If the perimeter of the rectangle is 48 cm, find its area.

Question 622247: The length of a rectangle is 6 cm longer than its width. If the perimeter of the rectangle is 48 cm, find its area.
Answer by math-vortex(648) (Show Source): You can put this solution on YOUR website!
Hi, there--
.
Here is one way to solve this problem.
.
Let W be the width of the rectangle.
Let L be the length of the rectangle.
.
We need to write two equations that use the information in the problem to model the situation.
.
The perimeter is 48 cm. Perimeter is the distance around the the rectangle: two widths and two lengths.
[two widths of the rectangle] + [two lengths of the rectangle] = [the perimeter]
.
In algebra, we write

.
We also know that the length of a rectangle is 6 cm longer than its width.
[the length of the rectangle] = [the width of the rectangle] + [6 more centimeters]
.
In algebra, we write,

.
Now we have a system of two equations. We will solve it using the substitution method. Substitute W+6 for L in the perimeter equation.
.

.
Simplify and solve for W. Clear the parentheses.

.
Combine like terms.

.
Subtract 12 form both sides of the equation.

.
Divide both sides of the equation by 4.

.
The width of the rectangle is 9 cm. Since the length of the rectangle is 6 more the the width, the length is 15 cm.
.
The formula for the area of a rectangle is A=L*W. The area is 135 square cm since 9*15=135.
.
The last step to to check our answer against the original problem. The perimeter should be 48 cm. We see that 2 widths is 18 cm, and 2 lengths is 30 cm; 18+30=48. Check!
.
Please email me if I need to explain any part of this better. By the way, there is a way to solve this problem without using two variables and a system of equations. Let me know if you'd like to see that method.
.
Ms.Figgy
math.in.the.vortex@gmail.com

RELATED QUESTIONS
Problem Page The length of a rectangle is 6 cm longer than its width. If the (answered by Cromlix)

The length of a rectangle is 4 cm longer than its width. If the perimeter of the... (answered by jorel1380)

The length of a rectangle is 3 cm longer than its width. If the perimeter of the... (answered by checkley79)

The length of a rectangle is 5 cm longer than its width. If the perimeter of... (answered by josgarithmetic,MathTherapy)

The length of a rectangle is 4 cm longer than its width. If the perimeter of the... (answered by TimothyLamb)

The length of a rectangle is 2 cm longer than its width. If the perimeter of the... (answered by ikleyn)

The length of a rectangle is 2 cm longer than its width. If the perimeter of... (answered by addingup)

The length of a rectangle is 2 cm longer than its width. If the perimeter of the... (answered by ikleyn)

A rectangle is 8 cm longer than it is wide. Find the dimensions of the rectangle if its... (answered by Grinnell,mananth)