Answer :

Using the Pythagorean Theorem, it is found that the value of k is of k = 2.

What does the problem give?

The problem gives a right triangle in which:

  • One leg is k.
  • The other leg is of [tex]3 + \sqrt{5} = 5.24[/tex].
  • The hypotenuse is of [tex]\sqrt{3} + \sqrt{15} = 5.61[/tex]

What is the Pythagorean Theorem?

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:

[tex]h^2 = l_1^2 + l_2^2[/tex]

Hence, the value of k can be found as follows:

k² + (5.24)² = (5.61)²

k² = (5.61)² - (5.24)²

k = sqrt((5.61)² - (5.24)²)

k = 2.

The value of k is of k = 2.

More can be learned about the Pythagorean Theorem at https://brainly.com/question/654982

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