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law of cosines can figure out diagonal from the triangle with the 34. Then, same for the left triangle to figure out what that 5x - 1 should be.
You know that the expression (5x-1) represents the hypotenuse of the triangles bounding the rectangle. Let's just look at the triangle STU. Since it is a triangle, the Pythagorean Theorem asserts that the expression (5x-1) measurement of the hypotenuse MUST be greater in magnitude than either of the length magnitudes of the vector ST or TU. Carefully check the values given to you as options in the problem. Assume the higher number 8.56, since all you need is a value of x such that \[5x-1\le 8.56\] is true. As soon as that is true, the figure is falsified and proven impossible. Only one value option of the four makes the above expression true. Can you see which one it is?
so A ? @AakashSudhakar
That's correct! X=1 is the only value that satisfies the inequality, which cannot be possible due to the nature of triangles.
i thought the arrow was the angle there.. sorry
For questions like these, you don't even need the rest of the rectangle or the angle measurement. All you need is the Pythagorean Theorem and the side values. Then it's just mathelogic from there.
Is STU a right triangle for sure?
Oh goodness! My apologies @DanJS, you may be right... I just noticed that the opposite sides ST and UR are unequal, which certainly throws a monkey wrench into my train of thought.
yes, but you had the right idea i think, the longer side has to be greater than the sum of the other two sides
i dont remember the property name
5x - 1 > 8.56 + 4.16 still A is correct..
So long as the answer isn't confounded. Hopefully @DanJS and I were of some help, @NessaGee