Answer:
• x = 9
• y = 6√2
Step-by-step explanation:
The right triangles are all similar, so the ratios of hypotenuse to short side are the same:
27/x = x/3
x^2 = 81 . . . . . multiply by 3x
x = 9 . . . . . . . . take the square root
Then y can be found from the Pythagorean theorem:
x^2 = y^2 + 3^2
81 - 9 = y^2 = 72 . . . . . subtract 9
y = √72 = 6√2 . . . . . . .take the square root
The values of x and y are 9 and 6√2, respectively.
