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  1. #1
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    Easiest Sum for You'll

    A rectangle has perimeter 92cm and the lenght of its diagnol is 34cm...Find it's area.....I'm studin in class 8 so......
    The answer which Iam getting is 480cm2 but the correct answer is 240...Can any1 solve it and tell me how you get it....Thx in advance
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  2. #2
    Senior Member nikhil's Avatar
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    Your answer is correct
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  3. #3
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    Quote Originally Posted by avincool View Post
    A rectangle has perimeter 92cm and the lenght of its diagnol is 34cm...Find it's area.....I'm studin in class 8 so......
    The answer which Iam getting is 480cm2 but the correct answer is 240...Can any1 solve it and tell me how you get it....Thx in advance
    It's a rectangle hence the 2 opposite side will have the same length. Lets call them x and y.

    The Perimeter is the total length of the rectangle hence the opposite sides multiplied by 2 therefore:

    2x +2y = 92 \ \ \ --(1)

    The diagonal is 34cm and by Pythagoras' theorem, we know that it is equal to the length squared hence:

    x^2 + y^2 = 34^2 \implies x^2 + y^2 = 1156 \ \ \ --(2)

    The equation (1) rearranges to give:

    x = 46 - y

    Substituting this x value into equation (2) gives:

    (46 - y)^2 + y^2 = 1156
    y^2 - 92y + 2116 + y^2 = 1156
    2y^2 - 92y + 960= 0
    y^2 - 46y +480 = 0
    (y - 30)(y - 16) = 0
    \therefore y = 30, \ y=16

    y= 30 \implies x = 16, \ y=16 \implies x=30

    Therefore the rectangle is of length and width of 30cm and 16cm respectfully.

    Area of rectangle = l \times w = 30 \times 16 = 480 \text{cm}^2
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  4. #4
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    Hello, avincool!

    A rectangle has perimeter 92cm and the lenght of its diagonal is 34cm.
    Find it's area.

    The answer which I am getting is 480 cm². . . . . Right!

    Let x = length, y = width.

    As Air pointed out, the perimeter is 92 cm.
    . . So we have: . 2x + 2y \:=\:92\quad\Rightarrow\quad x + y \:=\:46\;\;{\color{blue}[1]}

    The diagonal is 34.
    . . So we have: . x^2+y^2\:=\:34^2\quad\Rightarrow\quad x^2+y^2\:=\:1156\;\;{\color{blue}[2]}


    Sqaure [1]: . (x+y)^2 \:=\:46^2\quad\Rightarrow\quad x^2 + 2xy + y^2 \:=\:2116

    \text{So we have: }\;2xy + \underbrace{x^2+y^2}_{\text{This is 1156}\;{\color{blue}[2]}} \:=\:2116

    Hence: . 2xy + 1156 \:=\:2216\quad\Rightarrow\quad 2xy \:=\:960


    Therefore, the area of the rectangle is: . xy \:=\:480\text{ cm}^2

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