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Math Help - Algebra

  1. #1
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    Algebra

    1) The two sides of the right angle have lengths x and y. Represent the change in the triangle's area if the length of one side is doubled and the length of the other side is halved.

    2) The two equal sides of an isosceles triangle each have a length of 2x+3y-1. The perimeter of the triangle is 7x+9y. Determine the length of the third side.
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  2. #2
    Super Member ILikeSerena's Avatar
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    Re: Algebra

    Quote Originally Posted by darkangel06 View Post
    1) The two sides of the right angle have lengths x and y. Represent the change in the triangle's area if the length of one side is doubled and the length of the other side is halved.

    2) The two equal sides of an isosceles triangle each have a length of 2x+3y-1. The perimeter of the triangle is 7x+9y. Determine the length of the third side.
    Hi darkangel06!

    A rectangular triangle with sides x and y has an area of (1/2)xy.
    If I double x and half y, I get a rectangular triangle with sides (2x) and (1/2)y.
    Can you tell what the area is of that second triangle?
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  3. #3
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    Re: Algebra

    for the second one they did not mention the area of the triangle
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  4. #4
    Super Member ILikeSerena's Avatar
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    Re: Algebra

    Quote Originally Posted by darkangel06 View Post
    for the second one they did not mention the area of the triangle
    No, I didn't get to the second one yet.
    I decided to start with just the first one hoping for some feedback from you.
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  5. #5
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    Re: Algebra

    Oh! For the first one the area is just 0
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  6. #6
    Super Member ILikeSerena's Avatar
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    Re: Algebra

    Quote Originally Posted by darkangel06 View Post
    Oh! For the first one the area is just 0
    How did you get an area of 0?
    A triangle will always have an area that is greater than 0...
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  7. #7
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    Re: Algebra

    Well, that's what the answer is in the textbook and that's what i'm tryin to figure out :/
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  8. #8
    Super Member ILikeSerena's Avatar
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    Re: Algebra

    Quote Originally Posted by darkangel06 View Post
    Well, that's what the answer is in the textbook and that's what i'm tryin to figure out :/
    Ah! The change in area is 0 according to the answer in your textbook.
    But then you didn't answer my question yet: if I have a rectangular triangle with sides (2x) and (1/2)y, what is its area?
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  9. #9
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    Re: Algebra

    there is no area mentioned in the question !!!
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  10. #10
    Super Member ILikeSerena's Avatar
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    Re: Algebra

    Quote Originally Posted by darkangel06 View Post
    1) The two sides of the right angle have lengths x and y. Represent the change in the triangle's area if the length of one side is doubled and the length of the other side is halved.
    Quote Originally Posted by darkangel06 View Post
    there is no area mentioned in the question !!!
    Yes there is! See bolding.
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  11. #11
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    Re: Algebra

    I know. But the area is actually zero. That's what we have to find out. How is it zero.
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  12. #12
    Super Member ILikeSerena's Avatar
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    Re: Algebra

    Quote Originally Posted by darkangel06 View Post
    I know. But the area is actually zero. That's what we have to find out. How is it zero.
    Well, that was my point.
    The area is not zero.
    A triangle never has a zero area.
    In particular, the area of a rectangular triangle is \frac 1 2 \times (\text{length of one side}) \times (\text{length of the other side}).

    What do you get if you replace (\text{length of one side}) by (2x) and (\text{length of the other side}) by (\frac 1 2 y)?
    Last edited by ILikeSerena; February 27th 2013 at 02:44 PM.
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  13. #13
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    Re: Algebra

    It is a right angle not a rectangular triangle.
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  14. #14
    Super Member ILikeSerena's Avatar
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    Re: Algebra

    Quote Originally Posted by darkangel06 View Post
    It is a right angle not a rectangular triangle.
    I guess I should have called it a right triangle.
    Sorry, I'm not natively Canadian.
    I meant a triangle like the one in my avatar.
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  15. #15
    Super Member ILikeSerena's Avatar
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    Re: Algebra

    Oh wait!
    I meant I'm not natively Kuwaitian.
    (I had just looked up Brampton - first hit was Canada.)
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