SOLUTION: The perimeter of a rectangular garden is 98 feet. The length of the garden is 4 feet more than twice the width. What is the length of the garden?

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Question 224222: The perimeter of a rectangular garden is 98 feet. The length of the garden is 4 feet more than twice the width. What is the length of the garden?
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
The perimeter of a rectangular garden is 98 feet. The length of the garden is 4 feet more than twice the width. What is the length of the garden?

Step 1. The perimeter P means adding up all the four sides of a rectangle.

Step 2. Let w be the width.

Step 3. Let 2w+4 be the length

Step 4. Then, P=w+w+2w+4+2w+4=98.

Step 5. Solving yields the following steps

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


YOUR ANSWER


  • This is an equation! Solutions: w=15.
  • Graphical form: Equation w%2Bw%2B2w%2B4%2B2w%2B4=98 was fully solved.
  • Text form: w+w+2w+4+2w+4=98 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+w%2Bw%2B2w%2B4%2B2w%2B4=98+%29
    For tutors: simplify_cartoon( w+w+2w+4+2w+4=98 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at w%2Bw%2B2%2Aw%2Bhighlight_red%28+4+%29%2B2%2Aw%2Bhighlight_red%28+4+%29=98.
Added fractions or integers together
It becomes w%2Bw%2B2%2Aw%2Bhighlight_green%28+8+%29%2B2%2Aw=98.
Look at w%2Bw%2B2%2Aw%2Bhighlight_red%28+8+%29%2B2%2Aw=98.
Moved 8 to the right of expression
It becomes w%2Bw%2B2%2Aw%2B2%2Aw%2Bhighlight_green%28+8+%29=98.
Look at .
Eliminated similar terms highlight_red%28+w+%29,highlight_red%28+w+%29,highlight_red%28+2%2Aw+%29,highlight_red%28+2%2Aw+%29 replacing them with highlight_green%28+%281%2B1%2B2%2B2%29%2Aw+%29
It becomes highlight_green%28+%281%2B1%2B2%2B2%29%2Aw+%29%2B8=98.
Look at .
Added fractions or integers together
It becomes %28highlight_green%28+6+%29%29%2Aw%2B8=98.
Look at highlight_red%28+%28highlight_red%28+6+%29%29%2Aw+%29%2B8=98.
Remove unneeded parentheses around factor highlight_red%28+6+%29
It becomes highlight_green%28+6+%29%2Aw%2B8=98.
Look at 6%2Aw%2B8=highlight_red%28+98+%29.
Moved these terms to the left highlight_green%28+-98+%29
It becomes 6%2Aw%2B8-highlight_green%28+98+%29=0.
Look at 6%2Aw%2Bhighlight_red%28+8+%29-highlight_red%28+98+%29=0.
Added fractions or integers together
It becomes 6%2Aw%2Bhighlight_green%28+-90+%29=0.
Look at 6%2Aw%2Bhighlight_red%28+-90+%29=0.
Removed extra sign in front of -90
It becomes 6%2Aw-highlight_green%28+90+%29=0.
Look at highlight_red%28+6%2Aw-90+%29=0.
Solved linear equation highlight_red%28+6%2Aw-90=0+%29 equivalent to 6*w-90 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: w=15.

Universal Simplifier and Solver


Done!



For w=15 , then 2w+4=34 and P=2(15+34)=98 which is a true statement.

Step 6. ANSWER: The length is 34 feet.

I hope the above steps were helpful.

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And good luck in your studies!

Respectfully,
Dr J

drjctu@gmail.com

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