problem solving in RAE

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What is the area of a rectangle whose length is 1 unit longer than its width and whose diagonal is 2 unit longer than the width?

  • problem solving in RAE -

    looks like Pythagoras.

    width --- x
    length --- x+1
    diagonal --- x+2

    x^2 + (x+1)^2 = (x+2)^2

    by recognition:
    the sides are one unit apart, the only Pythagorean triple like that is 3,4,5, since 3^2 + 4^2 = 5^2.

    If you did not recognize that:
    x^2 + x^2 + 2x + 1 = x^2 + 4x + 4
    x^2 - 2x - 3 = 0

    (x - 3)(x+1) = 0
    x = 3 or x = -1, but a side can't be negative, so

    x = 3
    find the area using base*height

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