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Which value from the list below, when substituted for x, would represent an acute triangle with side lengths x, x+ 4, and 20? Assume that the longest side of the triangle is of length 20 units.

8
10
12
14

Respuesta :

Answer:

14 is the right answer

onyebuchinnaji

The value of x that will make triangle form actuate triangle is 14.

The given parameters:

  • First length of the triangle, a = x
  • Second length of the triangle, b = x + 4
  • Third length of the triangle, c = 20

For an acute triangle, the measure of each angle of the triangle must be less than 90 degrees.

Consider the angle opposite to the longest side to be 90⁰. The value of x will be determined using Pythagoras theorem.

[tex]x^2 + (x + 4)^2 = 20^2\\\\x^2 + x^2 + 8x+ 16 = 400\\\\2x^2 + 8x + 16 = 400\\\\x^2 + 4x + 8 = 200\\\\x^2 + 4x - 192= 0\\\\x^2 + 16x - 12x - 192 = 0\\\\x x + 16)-12(x + 16)= 0\\\\x = -16 \ \ or \ \ x = 12[/tex]

To reduce the angle opposite to the longest side 20 units, the value of x must be greater 12 units.

Thus, the value of x that will make triangle form actuate triangle is 14.

Learn more about sides of acute triangles here: https://brainly.com/question/2499350

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