Question

Please help me, I don't know how to do this...

Answer 1

Answer:

  A.  5

Step-by-step explanation:

The triangle will be a right triangle when the side lengths satisfy the Pythagorean theorem: the sum of the squares of the legs is equal to the square of the hypotenuse.

  (x +1)^2 +x^2 = (√61)^2

  x^2 +2x +1 +x^2 = 61 . . . eliminate parentheses

  2x^2 +2x = 60 . . . . . . .subtract 1, collect terms

  x^2 +x -30 = 0 . . . . . divide by 2, subtract 30

  (x +6)(x -5) = 0 . . . . factor the quadratic

  x = -6 or +5

The solution is x = 5.

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Side lengths cannot be negative. Solution values are values of x that make the factors zero. x+6=0 when x=-6, for example.