SOLUTION: I have a word problem to solve but not sure if I did it right. I may have used the wrong formula. Please show me the correct formula steps to solving this question?................

Question 386785: I have a word problem to solve but not sure if I did it right. I may have used the wrong formula. Please show me the correct formula steps to solving this question?......................I got the answer 4 x 9 but do not think it is correct.
The area of a rectangle is 14 square meters. Find the length and width of the rectangle if its length is 5 meters greater than its width. Use an equation and the formula for the
Area of a rectangle= (width)(length).

Found 3 solutions by stanbon, solver91311, rapaljer:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
The area of a rectangle is 14 square meters. Find the length and width of the rectangle if its length is 5 meters greater than its width. Use an equation and the formula for the Area of a rectangle= (width)(length).
----
Let the width be "x" meters.
Then the length is "x+5" meters.
----
Equation:
A = w*L
14 = x(x+5)
14 = x^2+5x
x^2+5x-14 = 0
Factor:
(x+7)(x-2) = 0
x = -7 of x = 2
---
Only the positive solution is meaningful.
width = 2 meters
length = 7 meters
===================
Cheers,
Stan H.

Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

4 by 9 can't be correct. 4 times 9 is 36, not 14.

Let represent the width of the rectangle. Then must represent the length. The area of the rectangle, given by multiplying length times width is 14, so:

Rearrange:

Now just solve the quadratic. Hint: It factors. Extra hint: 7 + (-2) = 5 and 7 X -2 = 14.

John

My calculator said it, I believe it, that settles it

Answer by rapaljer(4671)   (Show Source): You can put this solution on YOUR website!
Let x = width, since this is the last thing mentioned at the end of the first sentence.

Then the length is 5 more than the width, so
x+5 = length

Area = W*L
Area = x(x+5) = 14

This is a quadratic equation, so you have to multiply it out and set equal to zero. If you need help with solving quadratic equations by factoring, then you should see my website, which I will mention later. Meanwhile, this is what to do:
x^2 +5x=14
x^2+5x-14=0

Now, hopefully, it factors, and I think it does.
(x )(x )=0

(If you need help with factoring, then see my website!)
(x+7)(x-2)=0

There appear to be two solutions:
x+7=0
x=-7. This answer must be rejected, since you can't have a negative width.

The second solution works however,
x-2=0
x=2 meters, which is the width

So, this means that x+5=7 meters, which is the length.

The rectangle is 2 m. by 7 m., which is an area of 2*7 = 14 square meters.

If you need additional explanations, I recommend that you take a look at my own website. To see it click on my tutor name "rapaljer" anywhere in algebra.com. Look for the link to my website there. From my Homepage, look for the link "Basic, Intermediate, and College Algebra: One Step at a Time", click on "Basic Algebra," and then "Chapter 2," which is my chapter on FACTORING and also SOLVING QUADRATIC EQUATIONS. Several sections in this chapter apply to this particular problem. For a higher level of explanation, please take a look at my "Intermediate Algebra" and look in "Chapter 2" for Section 2.01 on factoring. See also the solutions of many of these exercises in the "MATH IN LIVING COLOR" pages, where the problems are solved in COLOR. My own students and others have been unanimous in telling me that my own explanations are easier to understand than the expensive textbooks that are written for mathematicians and publishers!! MY EXPLANATIONS WERE WRITTEN FOR STUDENTS WHO HAVE A HARD TIME UNDERSTANDING MATH!! And they are all FREE!!

There are also videos that might be helpful to you. To see all of my videos FREE (videos of me teaching in my younger years before I retired!!), look for "Rapalje Videos in Living Color." Choose either "Basic Algebra" or "Intermediate Algebra" and look for the topic "Factoring." Try the videos on a variety of topics from Basic, Intermediate, and College Algebra, especially LOGARITHMS from College Algebra. As I said, everything is FREE. I'm not only not SELLING anything! I'm not even ADVERTISING for anyone!!

I hope you like my website!!! If you do, please recommend it to your family and friends!! At least check out the JOKE PAGE--all safe jokes for the little ears in your family!!

Merry Christmas!!

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus

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