SOLUTION: the length of a rectangle is 4 centimeters more than the width. If both the width and the length were tripled, the area would be 108 square centimeters. Find the dimensions of the

Algebra ->  Rectangles -> SOLUTION: the length of a rectangle is 4 centimeters more than the width. If both the width and the length were tripled, the area would be 108 square centimeters. Find the dimensions of the       Log On


   

Question 1102565: the length of a rectangle is 4 centimeters more than the width. If both the width and the length were tripled, the area would be 108 square centimeters. Find the dimensions of the orginal rectangle
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


When the length and width are both tripled (multiplied by 3), the area is increased by a factor of 3*3=9. So the original area was 108/9=12.

Inspection shows that two numbers that differ by 4 and have a product of 12 are 2 and 6; those are the dimensions of the original rectangle.

If you need the formal algebra, it might look like this....

let x = original width
then x+4=original length
3x = new width
3(x+4) = 3x+12 = new length

The new area (length times width) is 108:
%283x%29%283x%2B12%29+=+108
9x%5E2%2B36x+=+108
9x%5E2%2B36x-108+=+0
x%5E2%2B4x-12+=+0
%28x%2B6%29%28x-2%29+=+0
x = -6 or x = 2;
reject the negative solution since it is the width The original width was x=2; the original length was x+4=6.

Learning how to solve the problem using formal algebra is good training, for when the problems get too complicated to solve informally by logical reasoning.

But you should also be able to use your powers of logical reasoning to solve simpler problems like this, without formal mathematical methods.