Question 902060: use a guess and check table:
Devin grew a rectangle on graph paper. The area of the rectangle is 810 square centimeters. The length is 3 centimeters greater than the width. Find the length and width of the rectangle.
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website! "Guess and check table"? One of the reasons for learning basic algebra is to be able to solve numerical problems more efficiently than guessing and checking.
L for length
w for width
L=w+3 and wL=810
 and .... that will be the only restriction for now.
Natural numbers will be used for the table, just for convenience although other real positive numbers would not be expected necessary.
w____________L____________AREA, w*L
_1____________4____________4
_2____________5____________10
_3____________6____________18
.
15___________18___________270
20___________23___________460
You can keep going this way until you find what you need.
That is an inferior way to find the dimensions when you understand the geometry and the number properties well enough.
__________________THE BETTR WAY____________________________
L=w+3, and w, the dimensions;
and wL=810.
Try to factorize 810.
810=10*81=2*5*9*9, but a list of all factors might be better.
ALL FACTORS: 2, 3 , 5, 6, 9, 10, 15, 18, 27, 30 45, 54, 81, 90, 135, 162, 270, 405;
The possible factorization which might work is  .
The meaningful solution here is  and  .
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