SOLUTION: Suppose that the length of a rectangle is three cm longer than twice the width and that the perimeter of the rectangle is 90 cm. a) Set up an equation for the perimeter involving

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Question 227757: Suppose that the length of a rectangle is three cm longer than twice the width and that the perimeter of the rectangle is 90 cm.
a) Set up an equation for the perimeter involving only W, the width of the rectangle.
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Suppose that the length of a rectangle is three cm longer than twice the width and that the perimeter of the rectangle is 90 cm.

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+3 be the length since the length is three cm longer than twice the width.

Step 4. Then, P=w+w+2w+3+2w+3=90.

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=14.
  • Graphical form: Equation w%2Bw%2B2w%2B3%2B2w%2B3=90 was fully solved.
  • Text form: w+w+2w+3+2w+3=90 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+w%2Bw%2B2w%2B3%2B2w%2B3=90+%29
    For tutors: simplify_cartoon( w+w+2w+3+2w+3=90 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at w%2Bw%2B2%2Aw%2Bhighlight_red%28+3+%29%2B2%2Aw%2Bhighlight_red%28+3+%29=90.
Added fractions or integers together
It becomes w%2Bw%2B2%2Aw%2Bhighlight_green%28+6+%29%2B2%2Aw=90.
Look at w%2Bw%2B2%2Aw%2Bhighlight_red%28+6+%29%2B2%2Aw=90.
Moved 6 to the right of expression
It becomes w%2Bw%2B2%2Aw%2B2%2Aw%2Bhighlight_green%28+6+%29=90.
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%2B6=90.
Look at .
Added fractions or integers together
It becomes %28highlight_green%28+6+%29%29%2Aw%2B6=90.
Look at highlight_red%28+%28highlight_red%28+6+%29%29%2Aw+%29%2B6=90.
Remove unneeded parentheses around factor highlight_red%28+6+%29
It becomes highlight_green%28+6+%29%2Aw%2B6=90.
Look at 6%2Aw%2B6=highlight_red%28+90+%29.
Moved these terms to the left highlight_green%28+-90+%29
It becomes 6%2Aw%2B6-highlight_green%28+90+%29=0.
Look at 6%2Aw%2Bhighlight_red%28+6+%29-highlight_red%28+90+%29=0.
Added fractions or integers together
It becomes 6%2Aw%2Bhighlight_green%28+-84+%29=0.
Look at 6%2Aw%2Bhighlight_red%28+-84+%29=0.
Removed extra sign in front of -84
It becomes 6%2Aw-highlight_green%28+84+%29=0.
Look at highlight_red%28+6%2Aw-84+%29=0.
Solved linear equation highlight_red%28+6%2Aw-84=0+%29 equivalent to 6*w-84 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: w=14.

Universal Simplifier and Solver


Done!



For w=14 , then 2w+3=31 and P=2(14+31)=90 which is a true statement.

Step 6. ANSWER: The width is 14 cm and the length is 31 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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http://www.Twitter.com/FreedomUTVep 1. Let w be the width