SOLUTION: The width, w, of a credit card is 3 centimeters shorter than the length, l. The area is 46.75 square centimeters. Find the perimeter.

Algebra ->  Rectangles -> SOLUTION: The width, w, of a credit card is 3 centimeters shorter than the length, l. The area is 46.75 square centimeters. Find the perimeter.      Log On


   

Question 1117602: The width, w, of a credit card is 3 centimeters shorter than the length, l. The area is 46.75 square centimeters. Find the perimeter.
Found 2 solutions by ikleyn, solver91311:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let x be the arithmetic mean of L and W (i.e., average of L and W).


Then  L = x + 1.5,  W = x - 1.5,   and the area is


L*W = (x+1.5)*(x-1.5) = x%5E2-2.25.


Hence, your equation for x is


x%5E2-2.25 = 46.75.


It gives  x%5E2 = 46.75 + 2.25 = 49;  Hence,  x = sqrt%2849%29 = 7.


Answer.  L = 7 + 1.5 = 8.5 cm;   W = 7 - 1.5 = 5.5 cm.

         The perimeter is  8.5 + 5.5 + 8.5 + 5.5 = 28 centimeters.

Solved   //   mentally.

===========
To see many other similar problems solved by the same method, look into the lesson
    - HOW TO solve the problem on quadratic equation mentally and avoid boring calculations
in this site.


Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Width:
Length:

Area is length times width



Put the quadratic in standard form and solve by any convenient means. Discard any negative zeros of the quadratic since there are no credit cards that have a negative width. However, it is instructive to note that the additive inverse of the negative zero is the length.

John

My calculator said it, I believe it, that settles it