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.

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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) About Me  (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

66=w%5E2%2B5w

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


66-66=w%5E2%2B5w-66


w%5E2%2B5w-66=0

We can use the quadratic formula given as

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ where

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

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B5x%2B-66+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%285%29%5E2-4%2A1%2A-66=289.

Discriminant d=289 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-5%2B-sqrt%28+289+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%285%29%2Bsqrt%28+289+%29%29%2F2%5C1+=+6
x%5B2%5D+=+%28-%285%29-sqrt%28+289+%29%29%2F2%5C1+=+-11

Quadratic expression 1x%5E2%2B5x%2B-66 can be factored:
1x%5E2%2B5x%2B-66+=+1%28x-6%29%2A%28x--11%29
Again, the answer is: 6, -11. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B5%2Ax%2B-66+%29



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