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anonymous
 one year ago
the length of a rectangle is 12m. lass than three times the width. the perimeter is 52cm. find the length of the rectangle
anonymous
 one year ago
the length of a rectangle is 12m. lass than three times the width. the perimeter is 52cm. find the length of the rectangle

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mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3Let the width = w Then the length is 3w  12 Ok so far?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3dw:1439866523893:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3There are two lengths with length 3w  12, and two widths with length w. Can you find the perimeter adding the lengths and the widths?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3No. Don't combine anything together. Just write all the lengths and widths that you added together on a line.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3dw: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
 one year ago
Best ResponseYou've already chosen the best response.0yea that makes more sense.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3When 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
 one year ago
Best ResponseYou've already chosen the best response.3That is the equation we get. It is a linear equation in one single variable, w. We can solve for w.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3\(3w  12 + 3w  12 + w + w = 52 \) 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
 one year ago
Best ResponseYou've already chosen the best response.3Add all terms in w: 3w + 3w + w + w Add all numbers: 12  12

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3What do you get for the sum of the terms in w?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3The 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
 one year ago
Best ResponseYou've already chosen the best response.33w + 3w + w + w = 8w 12 12 = 24

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3Ok, 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
 one year ago
Best ResponseYou've already chosen the best response.38w  24 = 52 +24 +24  8w = 76 Ok so far?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3For 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.
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