SOLUTION: the perimeter of a rectangle is 80 m. the length is 1 m more than twice the width. find the dimensions. what is the length? what is the width?

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Question 313116: the perimeter of a rectangle is 80 m. the length is 1 m more than twice the width. find the dimensions. what is the length? what is the width?
Found 2 solutions by ichudov, stanbon:
Answer by ichudov(507) About Me  (Show Source):
You can put this solution on YOUR website!
two sides are L and W.
perimeter is 2L+2W = 80.
L=1+2W
2(1+2W)+2W=80
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: W=13.
  • Graphical form: Equation 2%2A%281%2B2W%29%2B2W=80 was fully solved.
  • Text form: 2*(1+2W)+2W=80 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+2%2A%281%2B2W%29%2B2W=80+%29
    For tutors: simplify_cartoon( 2*(1+2W)+2W=80 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 2%2A%28highlight_red%28+1+%29%2B2%2AW%29%2B2%2AW=80.
Moved 1 to the right of expression
It becomes 2%2A%282%2AW%2Bhighlight_green%28+1+%29%29%2B2%2AW=80.
Look at 2%2A%282%2AW%2B1%29%2B2%2AW=highlight_red%28+80+%29.
Moved these terms to the left highlight_green%28+-80+%29
It becomes 2%2A%282%2AW%2B1%29%2B2%2AW-highlight_green%28+80+%29=0.
Look at highlight_red%28+2%2A%282%2AW%2B1%29+%29%2B2%2AW-80=0.
Expanded term 2 by using associative property on %282%2AW%2B1%29
It becomes highlight_green%28+2%2A2%2AW+%29%2Bhighlight_green%28+2%2A1+%29%2B2%2AW-80=0.
Look at highlight_red%28+2+%29%2Ahighlight_red%28+2+%29%2AW%2B2%2A1%2B2%2AW-80=0.
Multiplied numerator integers
It becomes highlight_green%28+4+%29%2AW%2B2%2A1%2B2%2AW-80=0.
Look at 4%2AW%2Bhighlight_red%28+2+%29%2Ahighlight_red%28+1+%29%2B2%2AW-80=0.
Multiplied numerator integers
It becomes 4%2AW%2Bhighlight_green%28+2+%29%2B2%2AW-80=0.
Look at 4%2AW%2Bhighlight_red%28+2+%29%2B2%2AW-highlight_red%28+80+%29=0.
Added fractions or integers together
It becomes 4%2AW%2Bhighlight_green%28+-78+%29%2B2%2AW=0.
Look at 4%2AW%2Bhighlight_red%28+-78+%29%2B2%2AW=0.
Moved -78 to the right of expression
It becomes 4%2AW%2B2%2AW%2Bhighlight_green%28+-78+%29=0.
Look at 4%2AW%2B2%2AW%2Bhighlight_red%28+-78+%29=0.
Removed extra sign in front of -78
It becomes 4%2AW%2B2%2AW-highlight_green%28+78+%29=0.
Look at highlight_red%28+4%2AW+%29%2Bhighlight_red%28+2%2AW+%29-78=0.
Eliminated similar terms highlight_red%28+4%2AW+%29,highlight_red%28+2%2AW+%29 replacing them with highlight_green%28+%284%2B2%29%2AW+%29
It becomes highlight_green%28+%284%2B2%29%2AW+%29-78=0.
Look at %28highlight_red%28+4+%29%2Bhighlight_red%28+2+%29%29%2AW-78=0.
Added fractions or integers together
It becomes %28highlight_green%28+6+%29%29%2AW-78=0.
Look at highlight_red%28+%28highlight_red%28+6+%29%29%2AW+%29-78=0.
Remove unneeded parentheses around factor highlight_red%28+6+%29
It becomes highlight_green%28+6+%29%2AW-78=0.
Look at highlight_red%28+6%2AW-78+%29=0.
Solved linear equation highlight_red%28+6%2AW-78=0+%29 equivalent to 6*W-78 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: W=13.

Universal Simplifier and Solver


Done!


W=13
L=1+2W=1+2*13=27

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
the perimeter of a rectangle is 80 m. the length is 1 m more than twice the width. find the dimensions. what is the length? what is the width?
---------------------
P = 2(L + W)
----
80 = 2((2W+1)+W)
40 = 3W+1
3W = 39
W = 13 m (width)
L = 2W+1 = 27 m (length)
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Cheers,
Stan H.
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