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) About Me  (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 x be the length and let 2x%2F3-3 be the width

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

Step 3. Then,

x%2Bx%2B%282x%2F3-3%29%2B%282x%2F3-3%29=114

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


YOUR ANSWER


  • This is an equation! Solutions: x=36.
  • Graphical form: Equation x%2Bx%2B%282x%2F3-3%29%2B%282x%2F3-3%29=114 was fully solved.
  • Text form: x+x+(2x/3-3)+(2x/3-3)=114 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+x%2Bx%2B%282x%2F3-3%29%2B%282x%2F3-3%29=114+%29
    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 x%2Bx%2Bhighlight_red%28+%282%2Ax%2F3-3%29+%29%2B%282%2Ax%2F3-3%29=114.
Remove unneeded parentheses around terms highlight_red%28+2%2Ax%2F3+%29,highlight_red%28+-3+%29
It becomes x%2Bx%2Bhighlight_green%28+2%2Ax%2F3+%29-highlight_green%28+3+%29%2B%282%2Ax%2F3-3%29=114.
Look at x%2Bx%2B2%2Ax%2F3-3%2Bhighlight_red%28+%282%2Ax%2F3-3%29+%29=114.
Remove unneeded parentheses around terms highlight_red%28+2%2Ax%2F3+%29,highlight_red%28+-3+%29
It becomes x%2Bx%2B2%2Ax%2F3-3%2Bhighlight_green%28+2%2Ax%2F3+%29-highlight_green%28+3+%29=114.
Look at x%2Bx%2B2%2Ax%2F3-highlight_red%28+3+%29%2B2%2Ax%2F3-highlight_red%28+3+%29=114.
Added fractions or integers together
It becomes x%2Bx%2B2%2Ax%2F3%2Bhighlight_green%28+-6+%29%2B2%2Ax%2F3=114.
Look at x%2Bx%2B2%2Ax%2F3%2Bhighlight_red%28+-6+%29%2B2%2Ax%2F3=114.
Moved -6 to the right of expression
It becomes x%2Bx%2B2%2Ax%2F3%2B2%2Ax%2F3%2Bhighlight_green%28+-6+%29=114.
Look at x%2Bx%2B2%2Ax%2F3%2B2%2Ax%2F3%2Bhighlight_red%28+-6+%29=114.
Removed extra sign in front of -6
It becomes x%2Bx%2B2%2Ax%2F3%2B2%2Ax%2F3-highlight_green%28+6+%29=114.
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 highlight_green%28+%281%2B1%2B2%2A1%2F3%2B2%2A1%2F3%29%2Ax+%29-6=114.
Look at %281%2B1%2Bhighlight_red%28+2+%29%2Ahighlight_red%28+1+%29%2F3%2B2%2A1%2F3%29%2Ax-6=114.
Multiplied numerator integers
It becomes %281%2B1%2Bhighlight_green%28+2+%29%2F3%2B2%2A1%2F3%29%2Ax-6=114.
Look at %281%2B1%2B2%2F3%2Bhighlight_red%28+2+%29%2Ahighlight_red%28+1+%29%2F3%29%2Ax-6=114.
Multiplied numerator integers
It becomes %281%2B1%2B2%2F3%2Bhighlight_green%28+2+%29%2F3%29%2Ax-6=114.
Look at .
Added fractions or integers together
It becomes %28highlight_green%28+10%2F3+%29%29%2Ax-6=114.
Look at highlight_red%28+%28highlight_red%28+10%2F3+%29%29%2Ax+%29-6=114.
Remove unneeded parentheses around factor highlight_red%28+10+%29,highlight_red%28+1%2F3+%29
It becomes highlight_green%28+10+%29%2Fhighlight_green%28+3+%29%2Ax-6=114.
Look at 10%2F3%2Ax-6=highlight_red%28+114+%29.
Moved these terms to the left highlight_green%28+-114+%29
It becomes 10%2F3%2Ax-6-highlight_green%28+114+%29=0.
Look at 10%2F3%2Ax-highlight_red%28+6+%29-highlight_red%28+114+%29=0.
Added fractions or integers together
It becomes 10%2F3%2Ax%2Bhighlight_green%28+-120+%29=0.
Look at 10%2F3%2Ax%2Bhighlight_red%28+-120+%29=0.
Removed extra sign in front of -120
It becomes 10%2F3%2Ax-highlight_green%28+120+%29=0.
Look at highlight_red%28+10%2F3%2Ax-120+%29=0.
Solved linear equation highlight_red%28+10%2F3%2Ax-120=0+%29 equivalent to 3.33333333333333*x-120 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=36.

Universal Simplifier and Solver


Done!



With x=36 , then 2x%2F3-3=2%2A36%2F3-3=24-3=21 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