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3 October, 15:03

The longer leg of a right triangle is 1 m longer than the shorter leg. The hypotenuse is 9 m longer than the shorter leg. Find the side lengths of the triangle.

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  1. 3 October, 15:22
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    Correct answer: c = 29 m, a = 21 m and b = 20 m

    Step-by-step explanation:

    Given:

    a = b + 1 longer leg a

    c = b + 9 hypotenuse c

    To solve this problem, we will use Pythagoras' theorem

    c² = a² + b²

    (b + 9) ² = (b + 1) ² + b²

    b² + 18 b + 81 = b² + 2 b + 1 + b²

    2 b² - b² + 2 b - 18 b + 1 - 81 = 0

    b² - 16 b - 80 = 0 we will factorize this equation

    ⇒ b² - 20 b + 4 b - 80 = b (b - 20) + 4 (b - 20) = (b - 20) · (b + 4) = 0

    (b - 20) · (b + 4) = 0 ⇒ b = 20 or b = - 4 false

    we accepted b = 20 m

    c = b + 9 = 20 + 9 = 29 m

    c = 29 m

    a = b + 1 = 20 + 1 = 21 m

    a = 21 m

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