document.write( "Question 214951: The length of a rectangular region is 20 meters less than four times its width. If the perimeter of the region is 135 meters, find the dimensions of the region. \n" ); document.write( "

Algebra.Com's Answer #162406 by drj(1380) $\"\"$ $\"About$

You can put this solution on YOUR website!
The length of a rectangular region is 20 meters less than four times its width. If the perimeter of the region is 135 meters, find the dimensions of the region.\r
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\n" ); document.write( "\n" ); document.write( "Step 1. Let w be the width and 4w-20 be the length.\r
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\n" ); document.write( "\n" ); document.write( "Step 2. Perimeter P means adding up the 4 sides of a rectangle or P=w+w+4w-20+4w-20=135.\r
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\n" ); document.write( "\n" ); document.write( "Step 3. The following will solve the equation in Step 2.\r
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Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

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\n" ); document.write( " YOUR ANSWER\n" ); document.write( "

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This is an equation! Solutions: w=17.5.
Graphical form: Equation $\"w%2Bw%2B4w-20%2B4w-20=135\"$ was fully solved.
Text form: w+w+4w-20+4w-20=135 simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+w%2Bw%2B4w-20%2B4w-20=135+%29\"$
For tutors: simplify_cartoon( w+w+4w-20+4w-20=135 )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"w%2Bw%2B4%2Aw-highlight_red%28+20+%29%2B4%2Aw-highlight_red%28+20+%29=135\"$ .
Added fractions or integers together
It becomes $\"w%2Bw%2B4%2Aw%2Bhighlight_green%28+-40+%29%2B4%2Aw=135\"$ .
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Look at $\"w%2Bw%2B4%2Aw%2Bhighlight_red%28+-40+%29%2B4%2Aw=135\"$ .
Moved $\"-40\"$ to the right of expression
It becomes $\"w%2Bw%2B4%2Aw%2B4%2Aw%2Bhighlight_green%28+-40+%29=135\"$ .
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Look at $\"w%2Bw%2B4%2Aw%2B4%2Aw%2Bhighlight_red%28+-40+%29=135\"$ .
Removed extra sign in front of $\"-40\"$
It becomes $\"w%2Bw%2B4%2Aw%2B4%2Aw-highlight_green%28+40+%29=135\"$ .
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Look at

.
Eliminated similar terms $\"highlight_red%28+w+%29\"$ , $\"highlight_red%28+w+%29\"$ , $\"highlight_red%28+4%2Aw+%29\"$ , $\"highlight_red%28+4%2Aw+%29\"$ replacing them with $\"highlight_green%28+%281%2B1%2B4%2B4%29%2Aw+%29\"$
It becomes $\"highlight_green%28+%281%2B1%2B4%2B4%29%2Aw+%29-40=135\"$ .
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Look at

.
Added fractions or integers together
It becomes $\"%28highlight_green%28+10+%29%29%2Aw-40=135\"$ .
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Look at $\"highlight_red%28+%28highlight_red%28+10+%29%29%2Aw+%29-40=135\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+10+%29\"$
It becomes $\"highlight_green%28+10+%29%2Aw-40=135\"$ .
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Look at $\"10%2Aw-40=highlight_red%28+135+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-135+%29\"$
It becomes $\"10%2Aw-40-highlight_green%28+135+%29=0\"$ .
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Look at $\"10%2Aw-highlight_red%28+40+%29-highlight_red%28+135+%29=0\"$ .
Added fractions or integers together
It becomes $\"10%2Aw%2Bhighlight_green%28+-175+%29=0\"$ .
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Look at $\"10%2Aw%2Bhighlight_red%28+-175+%29=0\"$ .
Removed extra sign in front of $\"-175\"$
It becomes $\"10%2Aw-highlight_green%28+175+%29=0\"$ .
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Look at $\"highlight_red%28+10%2Aw-175+%29=0\"$ .
Solved linear equation $\"highlight_red%28+10%2Aw-175=0+%29\"$ equivalent to 10*w-175 =0
It becomes $\"highlight_green%28+0+%29=0\"$ .
Result: $\"0=0\"$
\n" ); document.write( "This is an equation! Solutions: w=17.5.

Universal Simplifier and Solver

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Done!

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\n" ); document.write( "\n" ); document.write( "With w=17.5, then the length is 4w-20=4*17.5-20=50. Check if the perimeter leads to a true statement P=2*17.5+2*50=135 which is a true statement.\r
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\n" ); document.write( "\n" ); document.write( "Step 4. ANSWER. The width is 17.5 meters and the length is 50 meters.\r
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\n" ); document.write( "\n" ); document.write( "I hope the above steps were helpful.\r
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\n" ); document.write( "\n" ); document.write( "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.\r
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\n" ); document.write( "\n" ); document.write( "Good luck in your studies!\r
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\n" ); document.write( "\n" ); document.write( "Respectfully,
\n" ); document.write( "Dr J \n" ); document.write( "

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