In a right-triangle, the hypotenuse is 6 m more than twice the shortest side. If the third side is 2 m less than the hypotenuse, then the length of hypotenuse is ___ m .

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Solution

The correct option is C
26

Let $x$ be the length of the shortest side. Then, by question, hypotenuse and the third side measure $2 x + 6$ m and $(2 x + 6) - 2 = 2 x + 4$ m respectively.
Using Pythagoras' theorem, we have

$x^{2} + (2 x + 4)^{2} = (2 x + 6)^{2} .$

$\Rightarrow x^{2} + 4 x^{2} + 16 x + 16 = 4 x^{2} + 24 x + 36 5 x^{2} + 16 x + 16 = 4 x^{2} + 24 x + 36 x^{2} - 8 x - 20 = 0 (x - 10) (x + 2) = 0 x = - 2, 10$

Ignoring the negative solution as length of a side cannot be negative, we have $x$ = 10 m (shortest side).

Hypotenuse, $2 x + 6 = 2 (10) + 6 = 20 + 6 = 26 m .$

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