Question

Math question. Geometry

Answer 1

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