SOLUTION: the length of a rectangle is 8in.more than its width.the perimeter of the rectangle is 24 in. what are the width and length of the rectangle?

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Question 213893: the length of a rectangle is 8in.more than its width.the perimeter of the rectangle is 24 in. what are the width and length 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 8in. more than its width.the perimeter of the rectangle is 24 in. what are the width and length of the rectangle?

Step 1. Let l be the length where l=w+8 where w is the width.

Step 2. Perimeter of a rectangle is when the lengths of all four sides are summed together. Let P be the perimeter.

Step 3. Then we have

P=24=w%2B8%2Bw%2B8%2Bw%2Bw

Step 4. Solving the above equation for w yields

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


YOUR ANSWER


  • This is an equation! Solutions: w=2.
  • Graphical form: Equation 24=w%2B8%2Bw%2B8%2Bw%2Bw was fully solved.
  • Text form: 24=w+8+w+8+w+w simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+24=w%2B8%2Bw%2B8%2Bw%2Bw+%29
    For tutors: simplify_cartoon( 24=w+8+w+8+w+w )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 24=w%2Bhighlight_red%28+8+%29%2Bw%2Bhighlight_red%28+8+%29%2Bw%2Bw.
Added fractions or integers together
It becomes 24=w%2Bhighlight_green%28+16+%29%2Bw%2Bw%2Bw.
Look at 24=w%2Bhighlight_red%28+16+%29%2Bw%2Bw%2Bw.
Moved 16 to the right of expression
It becomes 24=w%2Bw%2Bw%2Bw%2Bhighlight_green%28+16+%29.
Look at .
Eliminated similar terms highlight_red%28+w+%29,highlight_red%28+w+%29,highlight_red%28+w+%29,highlight_red%28+w+%29 replacing them with highlight_green%28+%281%2B1%2B1%2B1%29%2Aw+%29
It becomes 24=highlight_green%28+%281%2B1%2B1%2B1%29%2Aw+%29%2B16.
Look at .
Added fractions or integers together
It becomes 24=%28highlight_green%28+4+%29%29%2Aw%2B16.
Look at 24=highlight_red%28+%28highlight_red%28+4+%29%29%2Aw+%29%2B16.
Remove unneeded parentheses around factor highlight_red%28+4+%29
It becomes 24=highlight_green%28+4+%29%2Aw%2B16.
Look at 24=highlight_red%28+4%2Aw%2B16+%29.
Moved these terms to the left highlight_green%28+-4%2Aw+%29,highlight_green%28+-16+%29
It becomes 24-highlight_green%28+4%2Aw+%29-highlight_green%28+16+%29=0.
Look at highlight_red%28+24+%29-4%2Aw-highlight_red%28+16+%29=0.
Added fractions or integers together
It becomes highlight_green%28+8+%29-4%2Aw=0.
Look at highlight_red%28+8+%29-4%2Aw=0.
Moved 8 to the right of expression
It becomes -4%2Aw%2Bhighlight_green%28+8+%29=0.
Look at highlight_red%28+-4%2Aw%2B8+%29=0.
Solved linear equation highlight_red%28+-4%2Aw%2B8=0+%29 equivalent to -4*w+8 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: w=2.

Universal Simplifier and Solver


Done!



Step 5. So width w=2 inches and length l=2+8=10 inches. Note Perimeter P=2(10+2)=24 inches

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J