algebra

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The length of a rectangle is 1 cm longer than its width. If the diagonal of the rectangle is 5 cm, what are the dimensions of the rectangle in centimeters? Enter your answers in the blanks. Enter only the numeric values rounded to the nearest tenth.

  • algebra -

    Let x be the short side, then the long side is (x+1).
    By Pythagoras theorem, the diagonal is
    √(x²+(x+1)²)
    =&radic(2x²+2x+1)=5
    Square both sides to get
    2x²+2x+1 = 5
    2(x²+x-2)=0
    2(x+2)(x-1)=0
    Solve for x and reject the root that is negative.

  • algebra-correction -

    Sorry, there was a mistake in the above solution. Here's the corrected version.

    √(x²+(x+1)²)
    =√(2x²+2x+1)=5

    Square both sides to get
    2x²+2x+1 = 25
    2(x²+x-12)=0
    2(x-3)(x+4)=0
    Solve for x and reject the root that is negative.

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