SOLUTION: The length of a rectangular room is 5 feet more than 3 times the width. The perimeter of the room is 62 feet. Find the dimensions of the room.

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Question 227666: The length of a rectangular room is 5 feet more than 3 times the width. The perimeter of the room is 62 feet. Find the dimensions of the room.
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
The length of a rectangular room is 5 feet more than 3 times the width. The perimeter of the room is 62 feet. Find the dimensions of the room.

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 3w+5 be the length since the length is 5 feet more than 3 times the width.

Step 4. Then, P=w+w+3w+5+3w+5=62.

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=6.5.
  • Graphical form: Equation w%2Bw%2B3w%2B5%2B3w%2B5=62 was fully solved.
  • Text form: w+w+3w+5+3w+5=62 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+w%2Bw%2B3w%2B5%2B3w%2B5=62+%29
    For tutors: simplify_cartoon( w+w+3w+5+3w+5=62 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at w%2Bw%2B3%2Aw%2Bhighlight_red%28+5+%29%2B3%2Aw%2Bhighlight_red%28+5+%29=62.
Added fractions or integers together
It becomes w%2Bw%2B3%2Aw%2Bhighlight_green%28+10+%29%2B3%2Aw=62.
Look at w%2Bw%2B3%2Aw%2Bhighlight_red%28+10+%29%2B3%2Aw=62.
Moved 10 to the right of expression
It becomes w%2Bw%2B3%2Aw%2B3%2Aw%2Bhighlight_green%28+10+%29=62.
Look at .
Eliminated similar terms highlight_red%28+w+%29,highlight_red%28+w+%29,highlight_red%28+3%2Aw+%29,highlight_red%28+3%2Aw+%29 replacing them with highlight_green%28+%281%2B1%2B3%2B3%29%2Aw+%29
It becomes highlight_green%28+%281%2B1%2B3%2B3%29%2Aw+%29%2B10=62.
Look at .
Added fractions or integers together
It becomes %28highlight_green%28+8+%29%29%2Aw%2B10=62.
Look at highlight_red%28+%28highlight_red%28+8+%29%29%2Aw+%29%2B10=62.
Remove unneeded parentheses around factor highlight_red%28+8+%29
It becomes highlight_green%28+8+%29%2Aw%2B10=62.
Look at 8%2Aw%2B10=highlight_red%28+62+%29.
Moved these terms to the left highlight_green%28+-62+%29
It becomes 8%2Aw%2B10-highlight_green%28+62+%29=0.
Look at 8%2Aw%2Bhighlight_red%28+10+%29-highlight_red%28+62+%29=0.
Added fractions or integers together
It becomes 8%2Aw%2Bhighlight_green%28+-52+%29=0.
Look at 8%2Aw%2Bhighlight_red%28+-52+%29=0.
Removed extra sign in front of -52
It becomes 8%2Aw-highlight_green%28+52+%29=0.
Look at highlight_red%28+8%2Aw-52+%29=0.
Solved linear equation highlight_red%28+8%2Aw-52=0+%29 equivalent to 8*w-52 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: w=6.5.

Universal Simplifier and Solver


Done!



For w=6.5 , then 3w+5=24.5 and P=2(6.5+24.5)=62 which is a true statement.

Step 6. ANSWER: The width is 6.5 feet and the length is 24.5 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

drjctu@gmail.com

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