Math Problem Solver

$$\begin{aligned}n &= - \frac{2 \sqrt{5}}{5}\\n &= \frac{2 \sqrt{5}}{5}\end{aligned}$$

First, simplify the equation.$$3 : 4 : 5 = 12 : n : n$$$$3 : 4 : 5=12 : n^{2} : 1$$

Match each term of the ratio on the left-hand side with its corresponding term on the right-hand side and express as fractions. $$\frac{3}{12} = \frac{4}{n^{2}} = \frac{5}{1}$$$$\frac{1}{4} = \frac{4}{n^{2}} = 5$$

Solve for the unknown using cross-multiplication. $$\begin{aligned}\frac{4}{n^{2}} &= 5 \\ 4 &= 5 n^{2} \\ n &= - \frac{2 \sqrt{5}}{5} \end{aligned}$$