a rectangle is 7cm longer than it is wide. The diagonal is 13 cm. What are the rectangle's dimensions?

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  • 9 years ago
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    Half of a rectangle is a right triangle, so you can use pythagoreans theorem.The diagonal will be the side opposite of the right angle (c).

    a^2 + b^2 = c^2

    say a is width and b is length.

    b = 7 + a since the rectangle is 7 cm longer than it is wide

    rearranging you get:

    a^2 + (7 + a)^2 = 13^2

    a^2 + 49 + 14a + a^2 = 169

    2(a^2) + 14 a - 120 = 0

    divide everything by 2:

    a^2 + 7a - 60 = 0

    factor:

    (a + 12)(a - 5) = 0

    so a = 5 or - 12

    since dimensions can't be negative, a = 5

    thus b = 5 + 7 = 12

    so the length is 12 cm and the width is 5 cm

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