Question

solve for x. figures are not necessarily drawn to scale.
solve for x

Explanation:

Step1: Identify similar triangles

∠F is common, ∠FGH=∠FDE=82°, so △FGH∽△FDE.

Step2: Set up proportion

$\frac{FG}{FD} = \frac{FH}{FE} = \frac{GH}{DE}$. Let FG = y, then FD = y + x. $\frac{y}{y+x} = \frac{4}{x} = \frac{6}{6+4.8} = \frac{6}{10.8} = \frac{5}{9}$.

Step3: Solve for x

$\frac{4}{x} = \frac{5}{9} \Rightarrow 5x = 36 \Rightarrow x = \frac{36}{5} = 7.2$.

Answer:

7.2