SOLUTION: The perimeter of a rectangle is 64 meters. the sum of the length and width is 32 meters. Find the length and width of the rectangle. Tried 2x+2y= 64 x+y=32...now what? Thanks so

Algebra ->  Rectangles -> SOLUTION: The perimeter of a rectangle is 64 meters. the sum of the length and width is 32 meters. Find the length and width of the rectangle. Tried 2x+2y= 64 x+y=32...now what? Thanks so      Log On


   

Question 223729: The perimeter of a rectangle is 64 meters. the sum of the length and width is 32 meters. Find the length and width of the rectangle.
Tried 2x+2y= 64
x+y=32...now what? Thanks so much!
Found 4 solutions by jim_thompson5910, rfer, drj, MathTherapy:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Take note that the same 'x's and 'y's are being used here. So we can use this fact to eliminate one variable so we can solve for the other. There are many ways to do this, but I'll use substitution.

x%2By=32 Start with the second equation


y=32-x Subtract 'x' from both sides.


2x%2B2y=64 Move onto the first equation.


2x%2B2highlight%28%2832-x%29%29=64 Plug in y=32-x. In other words, replace each 'y' with 32-x (this is possible since the two are equal).


So we now have the equation 2x%2B2%2832-x%29=64 which now consists of one variable. Simply solve this equation to find 'x'. I'll let you do that (let me know if you still need help). Once you find 'x', plug that value into y=32-x to find 'y'.

Answer by rfer(16322) About Me  (Show Source):
You can put this solution on YOUR website!
With what is given I think it must be a square.
I hope.
64/4=16 m per side

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
The perimeter of a rectangle is 64 meters. The sum of the length and width is 32 meters. Find the length and width of the rectangle.

Step 1. Perimeter P means adding up all 4 sides of a rectangle.

Step 2. Let w be the width.

Step 3. Let 32-w be the length.

Step 4. Then, P=w+w+w-32+w-32=4w-64=64

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


YOUR ANSWER


  • This is an equation! Solutions: w=32.
  • Graphical form: Equation 4w-64=64 was fully solved.
  • Text form: 4w-64=64 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+4w-64=64+%29
    For tutors: simplify_cartoon( 4w-64=64 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 4%2Aw-64=highlight_red%28+64+%29.
Moved these terms to the left highlight_green%28+-64+%29
It becomes 4%2Aw-64-highlight_green%28+64+%29=0.
Look at 4%2Aw-highlight_red%28+64+%29-highlight_red%28+64+%29=0.
Added fractions or integers together
It becomes 4%2Aw%2Bhighlight_green%28+-128+%29=0.
Look at 4%2Aw%2Bhighlight_red%28+-128+%29=0.
Removed extra sign in front of -128
It becomes 4%2Aw-highlight_green%28+128+%29=0.
Look at highlight_red%28+4%2Aw-128+%29=0.
Solved linear equation highlight_red%28+4%2Aw-128=0+%29 equivalent to 4*w-128 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: w=32.

Universal Simplifier and Solver


Done!



With w=32 and w-32=0. And P=2%2832%2B0%29=64 which is a true statement. But the answer is not realistic.

Step 5. ANSWER: The width is 32 meters and the length is 0 meters to satisfy the problem statement. So you were on the right track but note your equations are also identical if you multiply one of them by 2.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
The perimeter of a rectangle is 64 meters. the sum of the length and width is 32 meters. Find the length and width of the rectangle.
Tried 2x+2y= 64
x+y=32...now what? Thanks so much!

Let width of rectangle be W

Let length of rectangle be L

Since its perimeter = 64, then we can say that 2W + 2L = 64

Since it's also given that the sum of its width and length is 32, then we can say that W + L = 32

We now have 2 equations, as follows:
W + L = 32 -------- (i)
2W + 2L = 64 ------ (ii)
2W + 2L = 64 -------- (iii) ------ Multiplying eq (i) by 2

We can clearly see that the 2 equations are identical, which means that there are an infinite number of REAL numbers that can represent the length or the width of this rectangle. However, whatever length and width are given to the rectangle, they both have to be GREATER than 0, and their sum has to add to 32. In other words, if width = 10, then length = 22, or vice-versa. Likewise, if width were to be 1, then length = 31, and so on.

Therefore, we can say that the width of this rectangle = highlight_green%280+%3C+W+%3C+32%29, and that:

the length of this rectangle = highlight_green%28L+=+32+-+W%29, with W, or width being greater than 0.