How to solve for the length of a rectangle given its perimeter

Question
If the length of a rectangular parking lot is 10 meters less than twice the width, and the perimeter is 100 meters, find the length of the parking lot




Solution
First, write the word problem as an equation.
Let x = width of the rectangle
Then 2x - 10 = length of the rectangle
Then its perimeter is 2x + 2(2x - 10) = 100

The perimeter of a rectangle is computed as 2L + 2W

Simplify the above formula 2x + 4x - 20 = 100 ===> 6x = 120
Therefore x = 20

The length of the rectangle is 30 AND its width is 20.

Please do not forget to leave a feedback in Allexperts.com AND a comment in this blog.

Calculate the perimeter of the quadrilateral

Question
The perimeter of the quadrilateral is 120cm. Find the lengths and sides. (x+5)(x^2-3)(3x-8)(x+3).



Solution
Let us first define how to measure the perimeter of a quadrilateral. The perimeter of any quadrilateral, or any shape with four sides for that matter, is measured by adding the lengths of its sides. Hence, the quadrilateral on the right has a perimeter of 30 which is computed by adding the measure of its sides - 6 + 9 + 7 + 8.

Now, let us go back to our problem. The four sides of the quadrilateral are (x+5), (x^2-3), (3x-8) and (x+3). Hence, its perimeter is computed by (x+5) + (x^2-3) + (3x-8) + (x+3).

To solve for the length of the sides of the quadrilateral:

(x+5) + (x^2-3) + (3x-8) + (x+3) = 120
x^2 - 3+ x+5 + 3x - 8 + x + 3 = 120
x^2 + 5x - 3 = 120 ===> add like terms
x^2 + 5x - 123 = 0 ===> right side of the equation is set to zero
(x + ?) (x - ?) = 0 ====> to arrive at the root of the quadratic equation, think of two numbers that when you multiply them yields -123 and when you add them gives 5. Hmmm...difficult, however nothing prevents us to looking at a solution which is NOT a whole number.

Now, I got 13.87 and -8.87. Their multiple is -123.02 [close enough] and their sum is 5.

(x + 13.87) (x - 8.87) = 0
x = -13.87 ===> this is NOT an option because it is NEGATIVE.
x = 8.87

Now to calculate the lengths of the sides of the quadrilateral:
(x+5) ===> 13.87
(x^2-3) ==> 75.68
(3x-8) ===> 18.61
(x+3) ===> 11.87

Now to check whether the sum of the above is 120. 13.87 + 75.68 + 18.61 + 11.87 = 120.02 [close enough]

Please do not forget to leave a feedback in Allexperts.com AND a comment in this blog.




[Image via TPUB]