Question

What is the measure of n?5m15nn = [?]V==Give your answer in simplest form.Enter

Answer 1

In a diagram,

Thus, triangles ABC, ADB, and BDC are similar and the ratio between their corresponding sides is constant; therefore,

$n=DB,AD=5,DC=15,AB=m,AC=20$

Hence,

$\Rightarrow\frac{DB}{DC}=\frac{AD}{BD}=\frac{BA}{CB}$$\begin{gathered} \Rightarrow\frac{n}{15}=\frac{5}{n} \\ \Rightarrow n^2=5\cdot15=75 \\ \Rightarrow n^2=75 \\ \Rightarrow n=\sqrt[]{75}=5\sqrt[]{3} \\ \Rightarrow n=5\sqrt[]{3} \end{gathered}$

Thus, the answer is 3, n=5sqrt3