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- ([tex]\frac{a}{2}[/tex])² = [tex]\frac{3a^{2} }{4}[/tex]
⇒ [tex]\frac{3a^{2} }{4}[/tex] =10² {Since length of AD is given to be 10}
⇒ a²=[tex]\frac{100*4}{3}[/tex] = 133.333
⇒ a = 11.547
Hence, the length of CD = a/2 = 5.77. (Answer)
