Answer: Choice D) 7sqrt(3)
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Explanation:
The altitude of a triangle is the same as the height of a triangle.
Start with equilateral triangle ABC as shown in the attached image below. I have marked point D as the midpoint of side AB. The midpoint cuts that side into two equal parts, so AD = DB, both are 7 cm long. The other two sides are 14 cm.
The goal is to find the length of CD, which we'll call x for now.
Triangles ADC and BDC are right triangles.
Focus on either triangle ADC, or on triangle BDC, it doesn't matter as they are mirror copies of each other.
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a = 7
b = x
c = 14
Use the pythagorean theorem to solve for x
a^2 + b^2 = c^2
7^2 + x^2 = 14^2
49 + x^2 = 196
x^2 = 196 - 49
x^2 = 147
x = sqrt(147)
x = sqrt(49*3)
x = sqrt(49)*sqrt(3)
x = 7*sqrt(3)
