SOLUTION: the length of a rectangle is 2 km less than 3 times the width. if the perimeter is 68 km, what is the length of the rectangle?

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Question 222923: the length of a rectangle is 2 km less than 3 times the width. if the perimeter is 68 km, what is the length of the rectangle?
Answer by drj(1380)   (Show Source): You can put this solution on YOUR website!
The length of a rectangle is 2 km less than 3 times the width. If the perimeter is 68 km, what is the length of the rectangle?

Step 1. Perimeter P means adding up all the lengths of the sides of a rectangle.

Step 2. Let w be the width.

Step 3. Let 3w-2 be the length.

Step 4. Then P=w+w+3w-2+3w-2=68 km.

Step 5. Solving the equation in Step 4 leads to the following steps:

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


YOUR ANSWER


  • This is an equation! Solutions: w=9.
  • Graphical form: Equation was fully solved.
  • Text form: w+w+3w-2+3w-2=68 simplifies to 0=0
  • Cartoon (animation) form:
    For tutors: simplify_cartoon( w+w+3w-2+3w-2=68 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Added fractions or integers together
It becomes .
Look at .
Moved -4 to the right of expression
It becomes .
Look at .
Removed extra sign in front of -4
It becomes .
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 .
Look at .
Added fractions or integers together
It becomes .
Look at .
Remove unneeded parentheses around factor highlight_red%28+8+%29
It becomes .
Look at .
Moved these terms to the left highlight_green%28+-68+%29
It becomes .
Look at .
Added fractions or integers together
It becomes .
Look at .
Removed extra sign in front of -72
It becomes .
Look at .
Solved linear equation highlight_red%28+8%2Aw-72=0+%29 equivalent to 8*w-72 =0
It becomes .
Result:
This is an equation! Solutions: w=9.

Universal Simplifier and Solver


Done!



With w=9, then 3w-2=27-2=25 and P=2(9+25)=68... which is a true statement.

Step 6. ANSWER: Length is 25 kilometers.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J
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