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Hello, everyone. We're about to solve another application on non-linear systems.
The strategy for solving these is to find at least two formulas that relate to the problem.
Here is the problem:
A rectangle has an area up 36 square inches and a perimeter of 30 inches.
Find the dimensions (length and width) of the rectangle.
So, we're going to be working with a rectangle, with its length and with its width.
Alright, clearly we're going to be dealing with perimeter and areabecause that's the
information we were given. The perimeter of a rectangle
equals twice the length plus
twice the width,
and we're told the perimeter is 30
so 30 equals 2L + 2W.
Now notice that each number is divisible by 2, so I am going to divide by 2 in order to make
the numbers smaller. That will give us 15 = L + W. The other formula we're going to use is
the formula for the area of a rectangle because we were given that information.
L times W equals the area of a rectangle, so
in this case, L times W is going to equal 36.
Come back over to the perimeter formula and
we will solve for W. We get 15 - L.
I'm going to substitute that value for the W
in the area formula, so I'll have
L times 15 - L
equals 36.
Now I'll distribute: 15L - L squared
equals 36.
Using the zero principle,
we get the line the teacher is writing now.
Now, this is very easy to factor so I'm going to factor. However, you can also use the
Quadratic Formula. But since I'm factoring
I'm going to set each factor equal to zero.
For (L-3)(L-12) to equal zero, at least one of the factors must be equal to zero.
therefore L equals 38
and L equals 12. We have 2 possibilities.
We have to find out what the width is for each each value of L.
If L equals 3, I use the Area formula
(teacher reads what she is writing)
to find that W = 12.
If L equals 12
W = 3.
Clearly, the dimensions are 3 X 12 or
12 X 3.. Thus, W = 3, and L = 12.
Talk to you later.