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Math Help - Algebra Word Problem

  1. #1
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    Algebra Word Problem

    A rectangle is 4 times as long as it is wide. A second rectangle is 5 centimeters longer and 2 centimeters wider than the first. The area of the second rectangle is 270 square centimeters greater than the first. What are the dimensions of the original rectangle?

    I don't quite understand the correct process to go through when doing this, so could you show me how you get the answer? Thanks again guys!
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  2. #2
    Bar0n janvdl's Avatar
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    Quote Originally Posted by quartersworth View Post
    A rectangle is 4 times as long as it is wide. A second rectangle is 5 centimeters longer and 2 centimeters wider than the first. The area of the second rectangle is 270 square centimeters greater than the first. What are the dimensions of the original rectangle?

    I don't quite understand the correct process to go through when doing this, so could you show me how you get the answer? Thanks again guys!
    Rectangle 1:
    • L = 4x

    • W = x


    Rectangle 2:
    • L = 4x + 5

    • W = x + 2


    If the area = 270 then that means:

    (4x + 5)(x + 2) = 270

    Can you take it from here?
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  3. #3
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    Quote Originally Posted by janvdl View Post
    Rectangle 1:
    • L = 4x

    • W = x


    Rectangle 2:
    • L = 4x + 5

    • W = x + 2


    If the area = 270 then that means:

    (4x + 5)(x + 2) = 270

    Can you take it from here?
    How would you finish it?
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by quartersworth View Post
    How would you finish it?
    expand the brackets on the left. (take each term in the first set of brackets and multiply every term in the second set)

    by the way, janvdl made a slight error here, a minor oversight, i make them all the time. the question said "The area of the second rectangle is 270 square centimeters greater than the first"

    thus, the right side of the equation should be: 4x^2 + 270
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  5. #5
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    Quote Originally Posted by Jhevon View Post
    expand the brackets on the left. (take each term in the first set of brackets and multiply every term in the second set)

    by the way, janvdl made a slight error here, a minor oversight, i make them all the time. the question said "The area of the second rectangle is 270 square centimeters greater than the first"

    thus, the right side of the equation should be: 4x^2 + 270
    I guess the problem I am having is figuring out the end of the problem itself in my mind.
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by quartersworth View Post
    I guess the problem I am having is figuring out the end of the problem itself in my mind.
    show me what you've tried
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  7. #7
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    Quote Originally Posted by Jhevon View Post
    show me what you've tried
    I don't even know where to begin.
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  8. #8
    Bar0n janvdl's Avatar
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    Quote Originally Posted by janvdl View Post
    Rectangle 1:
    • L = 4x

    • W = x


    Rectangle 2:
    • L = 4x + 5

    • W = x + 2


    If the area = 270 then that means:

    (4x + 5)(x + 2) = 4x^2 + 270

    Can you take it from here?
    Thanks for that spot Jhevon. Heck the things i miss sometimes.

    (4x + 5)(x + 2) = 4x^2 + 270

    4x^2 + 8x + 5x + 10 = 4x^2 + 270

    13x + 10 = 270

    13x = 260

    x = 20
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