Using the Pythagorean Theorem, the height of the equilateral triangle is given by:
A. [tex]h = 7\sqrt{3}[/tex] inches.
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]
For this problem, we have that:
- The height is one side of the triangle.
- The other side is half the length, of 7 in.
- The hypotenuse is the length, of 14 in.
Hence the height is found as follows:
[tex]h^2 + 7^2 = 14^2[/tex]
[tex]h = \sqrt{147}[/tex]
[tex]h = \sqrt{49 \times 3}[/tex]
[tex]h = 7\sqrt{3}[/tex] inches.
More can be learned about the Pythagorean Theorem at https://brainly.com/question/654982
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