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1 September, 21:32

Un predio rectangular tiene un área de 5000 pies^2. Una diagonal entre las esquinas opuestas mide 10 pies mas que un lado del predio, cuáles son las dimensiones del predio?

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  1. 1 September, 21:41
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    106.08 and 47.13 feet

    Step-by-step explanation:

    We have that the area of a rectangle is equal to the multiplication of one side by the other side, that is:

    a = x * y

    we know that the area is 5000, therefore:

    5000 = x * y

    y = 5000 / x

    they tell us that the diagonal measures 10 feet more than one side, let's say on the x side, therefore the diagonal measures x + 10.

    A right triangle is formed, which by the Pythagorean equation has the following form:

    (x + 10) ^ 2 = x ^ 2 + y ^ 2

    if we replace the value of and we are left with:

    (x + 10) ^ 2 = x ^ 2 + (5000 / x) ^ 2

    x ^ 2 + 20 * x + 100 = x ^ 2 + 5000 ^ 2 / x ^ 2

    20 * x + 100 = 5000 ^ 2 / x ^ 2

    20 * x ^ 3 + 100 * x ^ 2 = 25000000

    from here we obtain that the value of x is equal to 106.08

    now the value of y:

    y = 5000 / 106.08

    y = 47.13

    therefore the measurements are 106.08 and 47.13 feet
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