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29 January, 13:17

If / 61 is the longest side length in the triangle, find the value of x that makes the triangle above a right triang

answer in simplest radical form.

A. 5

B. 6

C. 2V15

D. 6V10

+5
Answers (1)
  1. 29 January, 15:07
    0
    A. 5

    Step-by-step explanation:

    The longest side of the right triangle is the hypotenuse and it is √61 units. The other legs of the triangle is x unit and (x + 1) units.

    From Pythagoras theorem for right angle triangle, the square of the hypotenuse is equal to the sum of the square of the other sides of the triangle. This implies that:

    (√61) ² = (x) ² + (x + 1) ²

    x² + x² + 2x + 1 = 61

    2x² + 2x + 1 - 61 = 0

    2x² + 2x - 60 = 0

    Dividing through by 2 gives:

    x² + x - 30 = 0

    x² + 6x - 5x - 30 = 0

    x (x + 6) - 5 (x + 6) = 0

    (x-5) (x+6) = 0

    x-5 = 0 or x+6 = 0

    x = 5 or x = - 6

    Since the length of a side cannot be negative, x = 5 units
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