SOLUTION: suppose that the width of a rectangle is 3 centimeters less than two-thirds of its length. the perimeter of the rectangle is 114centimeters. find the length and width of the rectan

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Question 215278This question is from textbook intermediate algebra
: suppose that the width of a rectangle is 3 centimeters less than two-thirds of its length. the perimeter of the rectangle is 114centimeters. find the length and width of the rectangle. This question is from textbook intermediate algebra

Answer by drj(1380)   (Show Source): You can put this solution on YOUR website!
Suppose that the width of a rectangle is 3 centimeters less than two-thirds of its length. The perimeter of the rectangle is 114 centimeters. Find the length and width of the rectangle.

Step 1. Let be the length and let be the width

Step 2. Perimeter P means adding up all four sides of a rectangle.

Step 3. Then,



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


YOUR ANSWER


  • This is an equation! Solutions: x=36.
  • Graphical form: Equation was fully solved.
  • Text form: x+x+(2x/3-3)+(2x/3-3)=114 simplifies to 0=0
  • Cartoon (animation) form:
    For tutors: simplify_cartoon( x+x+(2x/3-3)+(2x/3-3)=114 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Remove unneeded parentheses around terms highlight_red%28+2%2Ax%2F3+%29,highlight_red%28+-3+%29
It becomes .
Look at .
Remove unneeded parentheses around terms highlight_red%28+2%2Ax%2F3+%29,highlight_red%28+-3+%29
It becomes .
Look at .
Added fractions or integers together
It becomes .
Look at .
Moved -6 to the right of expression
It becomes .
Look at .
Removed extra sign in front of -6
It becomes .
Look at .
Eliminated similar terms highlight_red%28+x+%29,highlight_red%28+x+%29,highlight_red%28+2%2Ax%2F3+%29,highlight_red%28+2%2Ax%2F3+%29 replacing them with highlight_green%28+%281%2B1%2B2%2A1%2F3%2B2%2A1%2F3%29%2Ax+%29
It becomes .
Look at .
Multiplied numerator integers
It becomes .
Look at .
Multiplied numerator integers
It becomes .
Look at .
Added fractions or integers together
It becomes .
Look at .
Remove unneeded parentheses around factor highlight_red%28+10+%29,highlight_red%28+1%2F3+%29
It becomes .
Look at .
Moved these terms to the left highlight_green%28+-114+%29
It becomes .
Look at .
Added fractions or integers together
It becomes .
Look at .
Removed extra sign in front of -120
It becomes .
Look at .
Solved linear equation highlight_red%28+10%2F3%2Ax-120=0+%29 equivalent to 3.33333333333333*x-120 =0
It becomes .
Result:
This is an equation! Solutions: x=36.

Universal Simplifier and Solver


Done!



With , then is

Step 4. The length is 36 cm and width is 21 cm

I hope the above steps were helpful.

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Good luck in your studies!

Respectfully,
Dr J
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