SOLUTION: The length of a rectangular region is 20 meters less than four times its width. If the perimeter of the region is 135 meters, find the dimensions of the region.

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Question 214951: The length of a rectangular region is 20 meters less than four times its width. If the perimeter of the region is 135 meters, find the dimensions of the region.
Found 2 solutions by drj, nerdybill:
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
The length of a rectangular region is 20 meters less than four times its width. If the perimeter of the region is 135 meters, find the dimensions of the region.

Step 1. Let w be the width and 4w-20 be the length.

Step 2. Perimeter P means adding up the 4 sides of a rectangle or P=w+w+4w-20+4w-20=135.

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

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


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: w=17.5.
  • Graphical form: Equation w%2Bw%2B4w-20%2B4w-20=135 was fully solved.
  • Text form: w+w+4w-20+4w-20=135 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+w%2Bw%2B4w-20%2B4w-20=135+%29
    For tutors: simplify_cartoon( w+w+4w-20+4w-20=135 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at w%2Bw%2B4%2Aw-highlight_red%28+20+%29%2B4%2Aw-highlight_red%28+20+%29=135.
Added fractions or integers together
It becomes w%2Bw%2B4%2Aw%2Bhighlight_green%28+-40+%29%2B4%2Aw=135.
Look at w%2Bw%2B4%2Aw%2Bhighlight_red%28+-40+%29%2B4%2Aw=135.
Moved -40 to the right of expression
It becomes w%2Bw%2B4%2Aw%2B4%2Aw%2Bhighlight_green%28+-40+%29=135.
Look at w%2Bw%2B4%2Aw%2B4%2Aw%2Bhighlight_red%28+-40+%29=135.
Removed extra sign in front of -40
It becomes w%2Bw%2B4%2Aw%2B4%2Aw-highlight_green%28+40+%29=135.
Look at highlight_red%28+w+%29%2Bhighlight_red%28+w+%29%2Bhighlight_red%28+4%2Aw+%29%2Bhighlight_red%28+4%2Aw+%29-40=135.
Eliminated similar terms highlight_red%28+w+%29,highlight_red%28+w+%29,highlight_red%28+4%2Aw+%29,highlight_red%28+4%2Aw+%29 replacing them with highlight_green%28+%281%2B1%2B4%2B4%29%2Aw+%29
It becomes highlight_green%28+%281%2B1%2B4%2B4%29%2Aw+%29-40=135.
Look at %28highlight_red%28+1+%29%2Bhighlight_red%28+1+%29%2Bhighlight_red%28+4+%29%2Bhighlight_red%28+4+%29%29%2Aw-40=135.
Added fractions or integers together
It becomes %28highlight_green%28+10+%29%29%2Aw-40=135.
Look at highlight_red%28+%28highlight_red%28+10+%29%29%2Aw+%29-40=135.
Remove unneeded parentheses around factor highlight_red%28+10+%29
It becomes highlight_green%28+10+%29%2Aw-40=135.
Look at 10%2Aw-40=highlight_red%28+135+%29.
Moved these terms to the left highlight_green%28+-135+%29
It becomes 10%2Aw-40-highlight_green%28+135+%29=0.
Look at 10%2Aw-highlight_red%28+40+%29-highlight_red%28+135+%29=0.
Added fractions or integers together
It becomes 10%2Aw%2Bhighlight_green%28+-175+%29=0.
Look at 10%2Aw%2Bhighlight_red%28+-175+%29=0.
Removed extra sign in front of -175
It becomes 10%2Aw-highlight_green%28+175+%29=0.
Look at highlight_red%28+10%2Aw-175+%29=0.
Solved linear equation highlight_red%28+10%2Aw-175=0+%29 equivalent to 10*w-175 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: w=17.5.

Universal Simplifier and Solver


Done!



With w=17.5, then the length is 4w-20=4*17.5-20=50. Check if the perimeter leads to a true statement P=2*17.5+2*50=135 which is a true statement.

Step 4. ANSWER. The width is 17.5 meters and the length is 50 meters.

I hope the above steps were helpful.

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Good luck in your studies!

Respectfully,
Dr J

Answer by nerdybill(5411) About Me  (Show Source):
You can put this solution on YOUR website!
The length of a rectangular region is 20 meters less than four times its width. If the perimeter of the region is 135 meters, find the dimensions of the region.
.
Let w = width
then from "length of a rectangular region is 20 meters less than four times its width" we get:
4w-20 = length
.
definition of perimeter:
2(width + length)
.
2(w + 4w-20) = 135
2(5w-20) = 135
10w-40 = 135
10w = 175
w = 17.5 meters (width)
.
Length:
4w-20 = 4(17.5)-20 = 50 meters (length)
.
Dimensions: 17.5 by 50 meters