SOLUTION: i need help on this word problem. One side of a rectangle is 4 in. longer than the other. If the sides are each increases by 2 in., the area of the new rectangle is 60 in^2. How lo

Question 788911: i need help on this word problem. One side of a rectangle is 4 in. longer than the other. If the sides are each increases by 2 in., the area of the new rectangle is 60 in^2. How long are the sides of the original rectangle?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
THE FIFT GRADER APPROACH:
If the length and the width of the rectangle are each increases by 2 in., in the larger final rectangle the length will still be 4 in. longer than the width.
So we are looking for two numbers (measurements in inches) that multiply to yield 60 (square inches) for the area of the rectangle.
, so the larger final rectangle is 6 inches wide by 10 inches long.
Then, the original smaller rectangle (before increasing each side by 2 inches) measured by .

MAKING IT LOOK MORE DIFFICULT WITH ALGEBRA:
= width of the original rectangle (in inches)
= length of the original rectangle (in inches)
As we increase each side by 2 inches, we get
= width of the new, larger rectangle (in inches)
= length of the new, larger rectangle (in inches)
= area of the new, larger rectangle (in square inches)
So, is our equation.
Simplifying:

Now we need to solve that quadratic equation and I can see 3 options.

Solving by factoring:

The solutions to that equation are
(from() and
and (from().
We discardthe solution because the lwidth of a recatngle (in inches) must be a positive number.
is the width of the original rectangle (in inches)
is the length of the original rectangle (in inches).

Completing the square:

is the length of the original rectangle in inches.
So, is the width of the original rectangle in inches.

Using the quadratic formula:
The solutions to an equation of the form can be calculated as

In the case of ,
, , and , so

One solution to that equation is
,
but that negative number cannot be the width of the original rectangle in inches.
The other solution is
and that is the width of the original rectangle in inches.
Then, is the length of the original rectangle in inches.
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