The length of CD in triangle ABC, where AB equals AC, BD is 5 cm, AB is 12 cm, and AD is 8 cm, is found to be 5 cm using the angle bisector theorem.
In triangle ABC, where AB is equal to AC and D is a point on BC, the provided details allow us to apply the angle bisector theorem. This theorem states that in a triangle with two equal sides, the angle bisector (AD in this case) divides the opposite side (BC) into segments that are proportional to the other two sides.
Let's denote the length of CD as x. Using the angle bisector theorem, we can set up a proportion: "BD over CD equals AB over AC."
Given that BD is 5 cm, AB is 12 cm, and AC is equal to AB (since AB equals AC), we can substitute these values into the proportion: "5 over x equals 12 over 12."
Cross-multiplying gives "5 times 12 equals x times 12." Solving for x, we get "x equals 5."
Therefore, the length of CD is 5 cm.
In summary, applying the angle bisector theorem in triangle ABC, we find that CD is 5 cm long.
The question probable may be:
In ΔABC , AB = AC and D is a point on BC . if BD = 5cm , AB = 12cm and AD = 8cm then the length of CD is?