SOLUTION: the perimeter of a rectangle is twice the sum of its length and its width. The perimeter is 28 meters and it's length is 2 meters more than twice it's width. What is it's length?

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: the perimeter of a rectangle is twice the sum of its length and its width. The perimeter is 28 meters and it's length is 2 meters more than twice it's width. What is it's length?      Log On


   

Question 204102: the perimeter of a rectangle is twice the sum of its length and its width. The perimeter is 28 meters and it's length is 2 meters more than twice it's width. What is it's length?
Found 2 solutions by ichudov, MathTherapy:
Answer by ichudov(507) About Me  (Show Source):
You can put this solution on YOUR website!
use L for length and W for width:
Perimeter is: 2*L + 2*W = 28.
Length is 2 meters more than twice the width: L = 2*W+2.
Use the above for length in the perimeter:
2*(2*W+2) + 2*W = 28.
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: W=4.
  • Graphical form: Equation 2%2A%282%2AW%2B2%29%2B2%2AW=28 was fully solved.
  • Text form: 2*(2*W+2)+2*W=28 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+2%2A%282%2AW%2B2%29%2B2%2AW=28+%29
    For tutors: simplify_cartoon( 2*(2*W+2)+2*W=28 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 2%2A%282%2AW%2B2%29%2B2%2AW=highlight_red%28+28+%29.
Moved these terms to the left highlight_green%28+-28+%29
It becomes 2%2A%282%2AW%2B2%29%2B2%2AW-highlight_green%28+28+%29=0.
Look at highlight_red%28+2%2A%282%2AW%2B2%29+%29%2B2%2AW-28=0.
Expanded term 2 by using associative property on %282%2AW%2B2%29
It becomes highlight_green%28+2%2A2%2AW+%29%2Bhighlight_green%28+2%2A2+%29%2B2%2AW-28=0.
Look at highlight_red%28+2+%29%2Ahighlight_red%28+2+%29%2AW%2B2%2A2%2B2%2AW-28=0.
Multiplied numerator integers
It becomes highlight_green%28+4+%29%2AW%2B2%2A2%2B2%2AW-28=0.
Look at 4%2AW%2Bhighlight_red%28+2+%29%2Ahighlight_red%28+2+%29%2B2%2AW-28=0.
Multiplied numerator integers
It becomes 4%2AW%2Bhighlight_green%28+4+%29%2B2%2AW-28=0.
Look at 4%2AW%2Bhighlight_red%28+4+%29%2B2%2AW-highlight_red%28+28+%29=0.
Added fractions or integers together
It becomes 4%2AW%2Bhighlight_green%28+-24+%29%2B2%2AW=0.
Look at 4%2AW%2Bhighlight_red%28+-24+%29%2B2%2AW=0.
Moved -24 to the right of expression
It becomes 4%2AW%2B2%2AW%2Bhighlight_green%28+-24+%29=0.
Look at 4%2AW%2B2%2AW%2Bhighlight_red%28+-24+%29=0.
Removed extra sign in front of -24
It becomes 4%2AW%2B2%2AW-highlight_green%28+24+%29=0.
Look at highlight_red%28+4%2AW+%29%2Bhighlight_red%28+2%2AW+%29-24=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+%29-24=0.
Look at %28highlight_red%28+4+%29%2Bhighlight_red%28+2+%29%29%2AW-24=0.
Added fractions or integers together
It becomes %28highlight_green%28+6+%29%29%2AW-24=0.
Look at highlight_red%28+%28highlight_red%28+6+%29%29%2AW+%29-24=0.
Remove unneeded parentheses around factor highlight_red%28+6+%29
It becomes highlight_green%28+6+%29%2AW-24=0.
Look at highlight_red%28+6%2AW-24+%29=0.
Solved linear equation highlight_red%28+6%2AW-24=0+%29 equivalent to 6*W-24 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: W=4.

Universal Simplifier and Solver


Done!


So, width = 4.
Since length = 2*W+2, length = 2*4+2 = 10.
Answer: Width = 4, length = 10.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Perimeter of a rectangle = twice its width + twice its length

Let width be w

Since length is 2 more than twice its width, then length = 2w + 2

2w + 2(2w + 2) = 28

2w + 4w + 4 = 28

6w = 24

w = 4

Since width is 4, then length is 2(4) + 2 = highlight_green%2810%29