Question

Triangle ABC is an equilateral triangle. BC = 10 What is the length of CD? Give your answer to the nearest whole number.

Answer 1

Since this is an equilateral triangle, we have AB = BC = 10. Then,

BD = AB/2 = 10/2 = 5

Now, we can use the Pythagorean theorem to find CD since BCD is a right triangle:

CD² + BD² = BC²

CD² = BC² - BD² = 10² - 5² = 100 - 25 = 75

CD = √75 = √(3 * 5 * 5) = √3 * √5² = 5√3 ≅ 8.66

As the question asks to give the answer to the nearest whole number, this answer is 9.