SOLUTION: The width of a rectangle is 6 less than twice its length. If the area of the rectangle is 113 cm^2, what is the length of the diagonal?

Question 218423: The width of a rectangle is 6 less than twice its length. If the area of the rectangle is 113 cm^2, what is the length of the diagonal?
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
The width of a rectangle is 6 less than twice its length. If the area of the rectangle is 113 cm^2, what is the length of the diagonal?

Step 1. Let L be the length.

Step 2. Let 2L-6 be the width since the width of a rectangle is 6 less than twice its length.

Step 3. Area A=113=L*(2L-6)

Step 4. Solving for L yields the following steps

Subtract 113 from both sides of the equation to get a quadratic equation

To solve for L, we can use the quadratic formula given as

where a=2, b=-6 and c=-113

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=940 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 9.16485485837795, -6.16485485837795. Here's your graph:

selecting the positive length
and

Step 5. Let c be the diagonal.

Step 6. Use the Pythagorean Theorem to find the diagonal which says that the sum of the squares of the legs (length and width in our example) is equal to the sum of the squares of the hypotenuse (diagonal in this case). That is,

Take the square root to both sides of the equation.

Step 7. ANSWER: The diagonal is 15.36 cm.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J
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