Question

solve for x. figures are not necessarily drawn to scale. (1 point) options: 8.8, 7.2, 2.2

Explanation:

Step1: Confirm similar triangles

$\angle F = \angle F$ (common angle), $\angle FGH = \angle FDE = 82^\circ$, so $\triangle FGH \sim \triangle FDE$ by AA similarity.

Step2: Set up proportion

Corresponding sides are proportional: $\frac{GH}{DE} = \frac{FH}{FE}$
First calculate $FE = FH + HE = 6 + 4.8 = 10.8$
Substitute values: $\frac{4}{x} = \frac{6}{10.8}$

Step3: Solve for x

Cross-multiply: $6x = 4 \times 10.8$
Calculate right-hand side: $4 \times 10.8 = 43.2$
Solve for x: $x = \frac{43.2}{6}$

Answer:

7.2