anonymous
  • anonymous
the length of a rectangle is 12m. lass than three times the width. the perimeter is 52cm. find the length of the rectangle
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
anonymous
  • anonymous
mathstudent55
  • mathstudent55
Let the width = w Then the length is 3w - 12 Ok so far?

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anonymous
  • anonymous
yes
mathstudent55
  • mathstudent55
|dw:1439866523893:dw|
mathstudent55
  • mathstudent55
There are two lengths with length 3w - 12, and two widths with length w. Can you find the perimeter adding the lengths and the widths?
anonymous
  • anonymous
9w?
mathstudent55
  • mathstudent55
No. Don't combine anything together. Just write all the lengths and widths that you added together on a line.
anonymous
  • anonymous
3w-12+3 +3w-12 +w?
mathstudent55
  • mathstudent55
|dw:1439866883780:dw| The two circled vertical sides are 3w - 12 + 3w - 12 The other two sides are w + w When you put it all together, you get: 3w - 12 + 3w - 12 + w + w Ok?
anonymous
  • anonymous
yea that makes more sense.
mathstudent55
  • mathstudent55
When you add the lengths of all sides, you get the perimeter. That expression we just got is the perimeter of the rectangle. We are told the perimeter is 52, so we set the expression for the perimeter equal to 52: 3w - 12 + 3w - 12 + w + w = 52
mathstudent55
  • mathstudent55
That is the equation we get. It is a linear equation in one single variable, w. We can solve for w.
mathstudent55
  • mathstudent55
\(3w - 12 + 3w - 12 + w + w = 52 \) We will solve it like we did before. Step 1. Combine like terms on both sides. In this case, there are like terms only on the left side, so let's work on the left side.
mathstudent55
  • mathstudent55
Add all terms in w: 3w + 3w + w + w Add all numbers: -12 - 12
mathstudent55
  • mathstudent55
What do you get for the sum of the terms in w?
anonymous
  • anonymous
-24
anonymous
  • anonymous
no sorry just 24
mathstudent55
  • mathstudent55
The terms in w are in red. The plain numbers are in green. \(\color{red}{3w} \color{green}{- 12} + \color{red}{3w} \color{green}{- 12} + \color{red}{w} + \color{red}{w} = 52\) \(\color{red}{3w + 3w + w + w} \color{green}{-12 - 12} = 52\) \(\color{red}{8w } \color{green}{-24} = 52\)
mathstudent55
  • mathstudent55
3w + 3w + w + w = 8w -12 -12 = -24
mathstudent55
  • mathstudent55
Ok, now we have \(8w - 24 = 52\) Step 2. Now we are ready for the next step. We need to move the number, -24, to the right side. To do that, we add 24 to both sides.
mathstudent55
  • mathstudent55
8w - 24 = 52 +24 +24 -------------- 8w = 76 Ok so far?
anonymous
  • anonymous
right.
mathstudent55
  • mathstudent55
For the final step, divide both sides by 8. You get w, the width. Then multiply w by 3 and subtract 12 to find the length.
anonymous
  • anonymous
THANKS. :)

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