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23 May, 19:14

The area of a square can be tripled by increasing the length and width by 10 inches. What is the original length of the square?

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  1. 23 May, 19:59
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    The new square has length: 10 + l, where l is the original length of the square, and it's area is (10 + l) ^2;

    So, we solve the equation: 3 x l^2 = (10 + l) ^2;

    Then, 3 x l^2 = 100 + 20 x l + l^2;

    Finally, 2xl^2 - 20xl - 100 = 0; / : 2;

    l^2 - 10l - 50 = 0 (we use the quadratic equation formula);

    The only positive solution is l = 5 (1 + / sqrt{3});
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