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

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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 · 2016-11-28T11:23:38

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]

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

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Explanation:

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