Answer:
2. x = √3
3. y = 3√2
4. a = (2/3)√2
Step-by-step explanation:
In an isosceles right triangle, the length of the hypotenuse is √2 times the length of one side. Said another way, the length of the side is 1/√2 times the length of the hypotenuse.
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2. x = √6/√2 = √(6/2) = √3 . . . . . divide the hypotenuse by √2 to find x
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3. (12 -√2y) = √2y . . . . . equate the hypotenuse to √2 times the leg and solve
12 = 2√2y
12/(2√2) = y = 6/√2 = 3√2
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4. 3a = 2√2 . . . . . . equate the hypotenuse to √2 times the leg and solve
a = 2√2/3 = (2/3)√2
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Comment on "rationalizing the denominator"
"Simplest radical form" usually means the radical is in the numerator. To eliminate it from the denominator, multiply by the radical:
1/√n = (√n)/(√n) · 1/√n = (√n)/(√n)^2 = (√n)/n
That is, ...
1/√2 = (√2)/2 . . . . for example.
