Question 1102565
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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.<br>
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.<br>
If you need the formal algebra, it might look like this....<br>
let x = original width
then x+4=original length
3x = new width
3(x+4) = 3x+12 = new length<br>
The new area (length times width) is 108:
{{{(3x)(3x+12) = 108}}}
{{{9x^2+36x = 108}}}
{{{9x^2+36x-108 = 0}}}
{{{x^2+4x-12 = 0}}}
{{{(x+6)(x-2) = 0}}}
x = -6 or x = 2;
reject the negative solution since it is the width<br<
The original width was x=2; the original length was x+4=6.<br>
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.<br>
But you should also be able to use your powers of logical reasoning to solve simpler problems like this, without formal mathematical methods.