Question

Glven: PA = PC and BA = BC. Use the diagram to find the length described.Suppose PA = 34 cm and PB = 16 cm. What is the length of AC?

Answer 1

We can calculate the length of AB using the Pythagorean Theorem, where:

$PA^2=AB^2+PB^2$

So, replacing PA by 34 and PB by 16 and solving for AB, we get:

$\begin{gathered} 34^2=AB^2+16^2 \\ 34^2-16^2=AB^2 \\ \sqrt{34^2-16^2}=AB \\ 30=AB \end{gathered}$

Then, AC = AB + BC, But AB = BC, so:

AC = 2*AB

Replacing AB by 30, we get:

AC = 2*30 = 60

Answer: AC=60