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.
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) (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.
Cartoon (animation) form: 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 . Added fractions or integers together It becomes . Look at . Moved to the right of expression It becomes . Look at . Removed extra sign in front of It becomes . Look at . Eliminated similar terms,,, replacing them with It becomes . Look at . Added fractions or integers together It becomes . Look at . Remove unneeded parentheses around factor It becomes . Look at . Moved these terms to the left It becomes . Look at . Added fractions or integers together It becomes . Look at . Removed extra sign in front of It becomes . Look at . Solved linear equation equivalent to 10*w-175 =0 It becomes . Result: 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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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