SOLUTION: The length of a rectangle is twice its width. If the perimeter of the rectangle is 60 ft , find its area

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Question 231989: The length of a rectangle is twice its width. If the perimeter of the rectangle is 60 ft , find its area
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
The length of a rectangle is twice its width. If the perimeter of the rectangle is 60 ft, find its area

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=60.

Step 5. Solving yields the following steps

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


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: w=10.
  • Graphical form: Equation w%2Bw%2B2w%2B2w=60 was fully solved.
  • Text form: w+w+2w+2w=60 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+w%2Bw%2B2w%2B2w=60+%29
    For tutors: simplify_cartoon( w+w+2w+2w=60 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+w+%29%2Bhighlight_red%28+w+%29%2Bhighlight_red%28+2%2Aw+%29%2Bhighlight_red%28+2%2Aw+%29=60.
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=60.
Look at %28highlight_red%28+1+%29%2Bhighlight_red%28+1+%29%2Bhighlight_red%28+2+%29%2Bhighlight_red%28+2+%29%29%2Aw=60.
Added fractions or integers together
It becomes %28highlight_green%28+6+%29%29%2Aw=60.
Look at highlight_red%28+%28highlight_red%28+6+%29%29%2Aw+%29=60.
Remove unneeded parentheses around factor highlight_red%28+6+%29
It becomes highlight_green%28+6+%29%2Aw=60.
Look at 6%2Aw=highlight_red%28+60+%29.
Moved these terms to the left highlight_green%28+-60+%29
It becomes 6%2Aw-highlight_green%28+60+%29=0.
Look at highlight_red%28+6%2Aw-60+%29=0.
Solved linear equation highlight_red%28+6%2Aw-60=0+%29 equivalent to 6*w-60 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: w=10.

Universal Simplifier and Solver


Done!



For w=10 , then 2w=20 and P=2(10+20)=60 which is a true statement.

Step 6. Area A is given as A=length * width = 20*10=200 square feet.

Step 7. ANSWER: The area is 200 square feet.

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


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