SOLUTION: If the AREA of a rectangle is 20m and the PERIMETER of the rectangle is 20m, what are the length and the width?

Question 214050: If the AREA of a rectangle is 20m and the PERIMETER of the rectangle is 20m, what are the length and the width?
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
If the AREA of a rectangle is 20 m^2 and the PERIMETER of the rectangle is 20 m, what are the length and the width?

Step 1. Area A=20=l*w where l is the length and w is the width for a rectangle.

Then l=20/w

Step 2. Perimeter P=20=l+l+2+2=2(l+w) where perimeter means adding up all four sides of a rectangle.

Step 3. Substitute the length l of Step 1 into Step 2 to get the following:

Simplify and multiply by w to both sides of equation to get rid of denominator

Subtract 10w to both sides of equation to get a quadratic equation.

where we can use the quadratic formula

where a=1 b=-10 and c=20

Step 4. The following steps will solve the quadratic equation.

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=20 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 7.23606797749979, 2.76393202250021. Here's your graph:

Step 5. ANSWER: Based on the above results, we have the width w=7.2361 m and the length l=2.7639 m. The numbers can also be reversed and note that these numbers satisfy the given area and perimeter.

So the sides of the rectangle are 7.2361 m and 2.7639 m.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

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