SOLUTION: The perimeter of a rectangle is 126 cm. The rectangle is twice as long as it is wide. What are its dimensions?

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Question 226249: The perimeter of a rectangle is 126 cm. The rectangle is twice as long as it is wide. What are its dimensions?
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
The perimeter of a rectangle is 126 cm. The rectangle is twice as long as it is wide. 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 be the length

Step 4. Then, P=w+w+2w+2w=126.

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=21.
  • Graphical form: Equation w%2Bw%2B2w%2B2w=126 was fully solved.
  • Text form: w+w+2w+2w=126 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+w%2Bw%2B2w%2B2w=126+%29
    For tutors: simplify_cartoon( w+w+2w+2w=126 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

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=126.
Look at .
Added fractions or integers together
It becomes %28highlight_green%28+6+%29%29%2Aw=126.
Look at highlight_red%28+%28highlight_red%28+6+%29%29%2Aw+%29=126.
Remove unneeded parentheses around factor highlight_red%28+6+%29
It becomes highlight_green%28+6+%29%2Aw=126.
Look at 6%2Aw=highlight_red%28+126+%29.
Moved these terms to the left highlight_green%28+-126+%29
It becomes 6%2Aw-highlight_green%28+126+%29=0.
Look at highlight_red%28+6%2Aw-126+%29=0.
Solved linear equation highlight_red%28+6%2Aw-126=0+%29 equivalent to 6*w-126 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: w=21.

Universal Simplifier and Solver


Done!



For w=21 , then 2w=42 and P=2(21+42)=126 which is a true statement.

Step 6. ANSWER: The width is 21 cm and the length is 42 cm.

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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