Question

A b and c midpoints of xyz. What is the length of ac

Answer 1

Consider the triangle ABX.

Determine the length of AX by using the pythagoras theorem.

`\begin{gathered} (AX)^2=(BX)^2-(AB)^2 \\ =(30)^2-(24)^2 \\ AX=\sqrt[]{324} \\ =18 \end{gathered}`

The length of XY is twice of side AX. So XY = 36

Consider trinagle XYZ.

Detertmine the length of side YZ by using pythagoras theorem.

`\begin{gathered} (YZ)^2=(60)^2-(36)^2 \\ YZ=\sqrt[]{2304} \\ =48 \end{gathered}`

The length of side YC is half of YZ so YC = 24.

Determine the length of side AC by using pyhtagras theorem in triangle AYC.

`\begin{gathered} AC=\sqrt[]{(AY)^2+(YC)^2} \\ =\sqrt[]{(18)^2+(24)^2} \\ =\sqrt[]{900} \\ =30 \end{gathered}`

So length of AC is 30.

Answer: 30