SOLUTION: the length of a rectangle garden is 5 m greater than the width. the area is 66m^2. find the dim. of the garden.

Question 214089: the length of a rectangle garden is 5 m greater than the width. the area is 66m^2. find the dim. of the garden.
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
The length of a rectangle garden is 5 m greater than the width. The area is 66m^2. Find the dimensions of the garden.

Step 1. Let w be the width and w+5 be the length.

Step 2. Let A=66=w(w+5) be the area of the rectangle.

Step 3. Solving for w yields the following steps

Subtract 66 from both sides of equation to yield a quadratic equation

We can use the quadratic formula given as

where

a=1, b=5 and c=-66

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=289 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 6, -11. Here's your graph:

Step 4. Based on the above steps, we select the positive solution 6. Now we have the width w=6 m and the length w+5=11 m. Area A=6*11=66 square meters as given in the problem

Step 5. ANSWER The dimensions of the rectangle are 6 m and 11 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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