Question

Triangle ABC is an equilateral triangle. AD = 10 What is the length of CD? Give your answer

Answer 1

Answer:

5.77

Step-by-step explanation:

In the triangle ABC, AD is perpendicular to BC and D is the midpoint of BC.  

Therefore, if all the sides of triangle ABC are 'a', then the length of CD will be  a/2.

Now, as ΔADC is a right triangle, then AD² +DC² =AC²

⇒ AD² = AC²- DC² =a²- ($\frac{a}{2}$)² = $\frac{3a^{2} }{4}$  

⇒ $\frac{3a^{2} }{4}$  =10² {Since length of AD is given to be 10}

⇒ a²=$\frac{100*4}{3}$ = 133.333

⇒ a = 11.547

Hence, the length of CD = a/2 = 5.77. (Answer)