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Find the exact value of x.

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baxthum8 eNotes educator | Certified Educator

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This is a special right triangle, called a 45˚-45˚-90˚.

In a 45-45-90 triangle the sides opposite 45˚ must be equal.  The ratios of the sides are 1:1:`sqrt(2).`

Since the hypotenuse is 5, to find the length of x, we would divide by `sqrt(2).`

`:. 5/sqrt(2)` Must rationalize the denominator.

`5/sqrt(2)*sqrt(2)/sqrt(2) = (5sqrt(2))/2`

The solution for x is `(5sqrt(2))/2.`

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flbyrne eNotes educator | Certified Educator

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This is an isosceles right triangle (45-45-90), where the two legs are equal and equal to

leg=leg=hypotenuse/`sqrt2`

Thus `x=5/sqrt2`

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alejandrogalarce | Student

This is an Isosceles right triangle 45-45-90, where the two legs are equal

`A^2 + B^2 = C^2`

`B^2 + B^2 = C^2`

`X^2 + (sqrt(2)) = 5`

thus

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