Find x if RY = x + 1, YT = 4x – 3 and SY = 2x. (Segment YS is the altitude drawn to hypotenuse RT.)?

Question

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9
2
-3
3

Answer 1

Please note that triangle TYS is similar to triangle SYR (angle STY = angle RSY, and angle TYS = angle SYR), thus TY/YS = YS/YR and therefore SY*SY = TY*YR
That is: 4x^2 = (x + 1)(4x - 3).
This is a quadratic equation and you can solve it readily to get:
x = 3