SOLUTION: The length of a new rectangular playing field is 5 yards longer than double the width. If the perimeter of the rectangular playing field is 340 yards, what are its dimensions? I ju

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Question 224323: The length of a new rectangular playing field is 5 yards longer than double the width. If the perimeter of the rectangular playing field is 340 yards, what are its dimensions? I just want to know how to figure the answer out. Please and thank you in advanced!
Found 2 solutions by rapaljer, drj:
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
This is a classic perimeter problem and I have TONS of these on my website--more about that later.

Let x= width of the rectangle
2x+5= length of the rectangle

2W + 2L= P
2(x) +2(2x+5)=340
2x+4x+10= 340
6x+10=340
6x=330
x=55 yards Width

2x+5= Length
2*55+5
110+5= 115 yards Length

Check: 2W+ 2L= 340
2*55+2*115=340
110+230=3340

It checks!!

As I mentioned, I have a COMPLETE explanation with examples and exercises with answers on my website!! To find my website, do a "Bing" Search for my last name "Rapalje". Look for "Rapalje Homepage" near the top of the search list. Then, near the top of my Homepage, look for "Basic, Intermediate and College Algebra: One Step at a Time," select "Basic Algebra" and in "Chapter 1", you will find a couple of sections on Word Problems. In particular, for Perimeter problems look in "Section 1.10 Word Problems, Part I" near the end of the section. This is my own non-traditional explanation that my own students have found MUCH easier to understand than the traditional textbooks. In addition to my explanations, examples and exercises, I have my "MATH IN LIVING COLOR" pages where I solved many of these exercises IN COLOR!!

R^2

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

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
The length of a new rectangular playing field is 5 yards longer than double the width. If the perimeter of the rectangular playing field is 340 yards, what are its dimensions?

Step 1. The perimeter P means adding up all the four sides of a rectangle.

Step 2. Let w be the width.

Step 3. Let 2w+5 be the length

Step 4. Then, P=w+w+2w+5+2w+5=340.

Step 5. Solving yields the following steps

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: w=55.
  • Graphical form: Equation w%2Bw%2B2w%2B5%2B2w%2B5=340 was fully solved.
  • Text form: w+w+2w+5+2w+5=340 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+w%2Bw%2B2w%2B5%2B2w%2B5=340+%29
    For tutors: simplify_cartoon( w+w+2w+5+2w+5=340 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at w%2Bw%2B2%2Aw%2Bhighlight_red%28+5+%29%2B2%2Aw%2Bhighlight_red%28+5+%29=340.
Added fractions or integers together
It becomes w%2Bw%2B2%2Aw%2Bhighlight_green%28+10+%29%2B2%2Aw=340.
Look at w%2Bw%2B2%2Aw%2Bhighlight_red%28+10+%29%2B2%2Aw=340.
Moved 10 to the right of expression
It becomes w%2Bw%2B2%2Aw%2B2%2Aw%2Bhighlight_green%28+10+%29=340.
Look at .
Eliminated similar terms highlight_red%28+w+%29,highlight_red%28+w+%29,highlight_red%28+2%2Aw+%29,highlight_red%28+2%2Aw+%29 replacing them with highlight_green%28+%281%2B1%2B2%2B2%29%2Aw+%29
It becomes highlight_green%28+%281%2B1%2B2%2B2%29%2Aw+%29%2B10=340.
Look at .
Added fractions or integers together
It becomes %28highlight_green%28+6+%29%29%2Aw%2B10=340.
Look at highlight_red%28+%28highlight_red%28+6+%29%29%2Aw+%29%2B10=340.
Remove unneeded parentheses around factor highlight_red%28+6+%29
It becomes highlight_green%28+6+%29%2Aw%2B10=340.
Look at 6%2Aw%2B10=highlight_red%28+340+%29.
Moved these terms to the left highlight_green%28+-340+%29
It becomes 6%2Aw%2B10-highlight_green%28+340+%29=0.
Look at 6%2Aw%2Bhighlight_red%28+10+%29-highlight_red%28+340+%29=0.
Added fractions or integers together
It becomes 6%2Aw%2Bhighlight_green%28+-330+%29=0.
Look at 6%2Aw%2Bhighlight_red%28+-330+%29=0.
Removed extra sign in front of -330
It becomes 6%2Aw-highlight_green%28+330+%29=0.
Look at highlight_red%28+6%2Aw-330+%29=0.
Solved linear equation highlight_red%28+6%2Aw-330=0+%29 equivalent to 6*w-330 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: w=55.

Universal Simplifier and Solver


Done!



For w=55 , then 2w+5=115 and P=2(55+115)=340 which is a true statement.

Step 6. ANSWER: The width is 55 yards and length is 115 yards.

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

drjctu@gmail.com

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