Question

question
solve for ( x ). figures are not necessarily drawn to scale.
(figure of a triangle with points f, g, h, d, e, angles at g and d are 82°, lengths: fh=6, gh=4, he=4.8, de=x)
answer attempt 1 out of 2
( x = ) input box submit answer

Explanation:

Step1: Identify Similar Triangles

Since $\angle FGH = \angle D = 82^\circ$ and $\angle F$ is common to both $\triangle FGH$ and $\triangle FDE$, by the AA (Angle - Angle) similarity criterion, $\triangle FGH \sim \triangle FDE$.

Step2: Set Up Proportion

For similar triangles, the ratios of corresponding sides are equal. The side $FH = 6$, $FE=FH + HE=6 + 4.8 = 10.8$, $GH = 4$, and $DE=x$. So we have the proportion $\frac{FH}{FE}=\frac{GH}{DE}$. Substituting the known values, we get $\frac{6}{10.8}=\frac{4}{x}$.

Step3: Solve for $x$

Cross - multiply the proportion: $6x=10.8\times4$. Calculate $10.8\times4 = 43.2$. Then, $x=\frac{43.2}{6}=7.2$.

Answer:

$x = 7.2$