Question

Given that line CD is a perpendicular bisector of triangle ABC, if side AB has a length of 9 cm and side AC has a length of 16 cm, What is the length of side CD? Answer to the nearest hundredth.

A 13.25 cm B 15.35 cm C 15.55 cm D 16.75 cm ​

Answer 1

C, 15.35 cm

Explanation:

By the definition of a perpendicular bisector, AD is equal to DB. This means that AD is half of AB. Thus;

AD = 4.5 cm

DB = 4.5 cm

It is given that AC is 16 cm and that Triangle CDA is a right triangle. By the Pythagorean Theorem:

`4.5^(2) + x^(2) = 16^2`

Simplify:

`20.25 + x^2 = 256\\x^2 = 235.75\\x = 15.35`

So the correct answer is 15.35 cm.