Question

The legs of a right triangle are represented by `x+sqrt2, x-sqrt2`. What is the length of the hypotenuse?

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Answer 1

The length of hypotenuse is `sqrt(2(x^2+2))`

Explanation:

Let hypotenuse is `h` and legs are `l_1 and l_2`
`h^2=l_1^2+l_2^2= (x+sqrt2)^2+ (x-sqrt2)^2 =x^2+cancel(2sqrt2x)+2 +x^2-cancel(2sqrt2x)+2 =2x^2+4=2(x^2+2) :. h=sqrt(2(x^2+2))` [Ans]