Question

Triangle ABC is an equilateral triangle.

AD = 10
What is the length of CD? Give your answer

Answer 1

5.77

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- (
`(a)/(2)`)² =
`(3a^(2) )/(4)`

⇒
`(3a^(2) )/(4)` =10² {Since length of AD is given to be 10}

⇒ a²=
`(100*4)/(3)` = 133.333

⇒ a = 11.547

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