Question

ABC is right angled at B, and D is a point on BC. if AD=18cm, BD= 9cm and CD=4cm, find AC

Answer 1

Task: ABC is right angled at B, and D is a point on BC. if AD=18cm, BD= 9cm and CD=4cm, find AC.

Solution:

From ABD, by using Pythagorean theorem: $|AB| = \sqrt{|AD|^2 - |BD|^2} = \sqrt{18^2 - 9^2} = \sqrt{2^29^2 - 9^2} = 9\sqrt{4 - 1} = 9\sqrt{3}$ (cm)

Therefore, from ABC we can find AC: $|AC| = \sqrt{|AB|^2 + |BC|^2} = \sqrt{\left(9\sqrt{3}\right)^2 + (|BD| + |DC|)^2} = \sqrt{3*81 + (4 + 9)^2} = \sqrt{243 + 13^2} = \sqrt{243 + 169} = \sqrt{412} = \sqrt{4*103} = 2\sqrt{103}$ (cm)

Answer: AC is $2\sqrt{103}$ cm