Question

What does m=? I could figure out n but I can’t seem to figure out m

Answer 1

The given figure can be redrawn as:

In the above figure, triangle BAD is similar to triangle CBD.

Therefore, the ratio of corresponding sides of the triangles CBD and ABD will be equal.

`(CB)/(AB)=(BD)/(AD)=(CD)/(BD)`

Hence,

`\begin{gathered} (BD)/(AD)=(CD)/(BD) \\ BD^2=AD* CD \\ n^2=5*15 \\ n^2=75 \end{gathered}`

Now applying Pythagoras theoerm to right triangle BAD,

`\begin{gathered} AB^2=BD^2+AD^2 \\ m^2=n^2+5^2 \\ m^2=75+25 \end{gathered}`

Solve the equation to find m.

`\begin{gathered} m^2=100 \\ m=\sqrt[]{100} \\ m=10 \end{gathered}`

Therefore, the value of m is 10.