9514 1404 393
Answer:
B. 4
Step-by-step explanation:
There are a couple of ways you can look at this question.
Triangle relationships
The value of x must satisfy the requirements of the triangle inequality, and that the legs of the triangle are shorter than the hypotenuse.
(x -1) +(2x -4) > (x -1) +2 ⇒ x > 3 . . . . from UW +UV > VW
2x -4 < (x -1) +2 ⇒ x < 5 . . . . from UV < VW
The only integer strictly between 3 and 5 is ...
x = 4 . . . . . . . gives a 3-4-5 right triangle
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Pythagorean theorem
The side lengths of this right triangle must satisfy the Pythagorean theorem:
UW² +UV² = VW²
(x -1)² +(2x -4)² = ((x -1) +2)²
x² -2x +1 +4x² -16x +16 = x² +2x +1
4x² -20x +16 = 0 . . . . . put in standard form
4(x -4)(x -1) = 0 . . . . . . .factor
Solutions are x = 4 and x = 1. Only the solution x = 4 is viable in this geometry.
x = 4
