Answer:
Step-by-step explanation:
Step 1: Find AB Use Pythagoras Theorem
AB = [tex]\sqrt{AC^{2} -BC^{2} } = \sqrt{12^{2} -8^{2} } = \sqrt{80}[/tex]
Step 2: Find the Area of the triangle ABC
Area = [tex]\frac{1}{2}AB.BC = \frac{1}{2}\sqrt{80}.8 = 4\sqrt{80}[/tex] = [tex]16\sqrt{5}[/tex]
Step 3: Find BD. Use the area of the triangle above
Area = [tex]\frac{1}{2}BD.AC[/tex]
We already known the Area and AC so, we just plug all the number in
BD = [tex]\frac{2. Area}{AC}[/tex] = [tex]\frac{2.16\sqrt{5}}{12}[/tex] = [tex]\frac{8\sqrt{5}}{3}[/tex]
Step 4: Find DC. Use Pythagoras Theorem of the triangle BDC
DC = [tex]\sqrt{BC^{2}-BD^{2} }[/tex] = [tex]\sqrt{8^{2}-(\frac{8\sqrt{5}}{3})^{2}}[/tex] = [tex]\frac{16}{3}[/tex]
