SOLUTION: The length of a rectangle is 5 cm less than 3 times the width. If the perimeter of the rectangle is 46 cm find the dimensions of the rectangle.

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Question 214680: The length of a rectangle is 5 cm less than 3 times the width. If the perimeter of the rectangle is 46 cm find the dimensions of the rectangle.
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
The length of a rectangle is 5 cm less than 3 times the width. If the perimeter of the rectangle is 46 cm find the dimensions of the rectangle.

Step 1. Let w be the width and let 3w-5 be the length as given in the problem.

Step 2. The perimeter P of a rectangle means to add up all the sides. So

P=w%2Bw%2B3w-5%2B3w-5=46

Step 3. The following will solve the equation in Step 2.

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


YOUR ANSWER


  • This is an equation! Solutions: w=7.
  • Graphical form: Equation w%2Bw%2B3w-5%2B3w-5=46 was fully solved.
  • Text form: w+w+3w-5+3w-5=46 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+w%2Bw%2B3w-5%2B3w-5=46+%29
    For tutors: simplify_cartoon( w+w+3w-5+3w-5=46 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at w%2Bw%2B3%2Aw-highlight_red%28+5+%29%2B3%2Aw-highlight_red%28+5+%29=46.
Added fractions or integers together
It becomes w%2Bw%2B3%2Aw%2Bhighlight_green%28+-10+%29%2B3%2Aw=46.
Look at w%2Bw%2B3%2Aw%2Bhighlight_red%28+-10+%29%2B3%2Aw=46.
Moved -10 to the right of expression
It becomes w%2Bw%2B3%2Aw%2B3%2Aw%2Bhighlight_green%28+-10+%29=46.
Look at w%2Bw%2B3%2Aw%2B3%2Aw%2Bhighlight_red%28+-10+%29=46.
Removed extra sign in front of -10
It becomes w%2Bw%2B3%2Aw%2B3%2Aw-highlight_green%28+10+%29=46.
Look at .
Eliminated similar terms highlight_red%28+w+%29,highlight_red%28+w+%29,highlight_red%28+3%2Aw+%29,highlight_red%28+3%2Aw+%29 replacing them with highlight_green%28+%281%2B1%2B3%2B3%29%2Aw+%29
It becomes highlight_green%28+%281%2B1%2B3%2B3%29%2Aw+%29-10=46.
Look at .
Added fractions or integers together
It becomes %28highlight_green%28+8+%29%29%2Aw-10=46.
Look at highlight_red%28+%28highlight_red%28+8+%29%29%2Aw+%29-10=46.
Remove unneeded parentheses around factor highlight_red%28+8+%29
It becomes highlight_green%28+8+%29%2Aw-10=46.
Look at 8%2Aw-10=highlight_red%28+46+%29.
Moved these terms to the left highlight_green%28+-46+%29
It becomes 8%2Aw-10-highlight_green%28+46+%29=0.
Look at 8%2Aw-highlight_red%28+10+%29-highlight_red%28+46+%29=0.
Added fractions or integers together
It becomes 8%2Aw%2Bhighlight_green%28+-56+%29=0.
Look at 8%2Aw%2Bhighlight_red%28+-56+%29=0.
Removed extra sign in front of -56
It becomes 8%2Aw-highlight_green%28+56+%29=0.
Look at highlight_red%28+8%2Aw-56+%29=0.
Solved linear equation highlight_red%28+8%2Aw-56=0+%29 equivalent to 8*w-56 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: w=7.

Universal Simplifier and Solver


Done!



With w=7 then the length is 3w-5=3*7-5=16. Note that these dimensions will result in a perimeter of 46 cm

Step 4. ANSWER: 7 cm is the width and 16 cm is the length of the rectangle

I hope the above steps were helpful.

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And good luck in your studies!

Respectfully,
Dr J