SOLUTION: A rectangular ink pad has a perimeter of 40 centimeters. Its area is 96 square centimeters. What are the dimensions of the ink pad?

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Question 1193307: A rectangular ink pad has a perimeter of 40 centimeters. Its area is 96 square centimeters. What are the dimensions of the ink pad?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52798)   (Show Source): You can put this solution on YOUR website!
.
A rectangular ink pad has a perimeter of 40 centimeters. Its area is 96 square centimeters.
What are the dimensions of the ink pad?
~~~~~~~~~~~~~~~ 

Let x be the length, y be the width.

Then x + y = 40/2 = 20 cm  (half of the perimeter).


So, the width is  y = 20-x cm.


Therefore, the area is xy = x*(20-x) = 96 cm^2.



So,  your area equation to find the length  x  is

    x*(20-x) = 96

    x^2 - 20x + 96 = 0

    (x-12)*(x-8) = 0


The roots are x= 12  and  x= 8.


ANSWER.  The dimensions of the pad are 12 cm  and  8 cm.

Solved.

--------------------

To see many similar solved problems,  look into the lesson
    - Problems on the area and the dimensions of a rectangle
in this site.



Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


The other tutor showed a solution using a method that you would likely see in a typical algebra textbook.

Here is another method that can be used that often makes the work required to solve the problem easier.

The perimeter is 40, so the average side length is 40/4=10. So

let 10+x = length
let 10-x = width

The area is 96:






ANSWER: The length is 10+x=12; the width is 10-x=8
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