Question

in the diagram below, gh is parallel to de. solve for x. round your answer to the nearest tenth if necessary.
answer attempt 2 out of 2
x =
submit answer

Explanation:

Step1: Set up proportion via similarity

Since $GH \parallel DE$, $\triangle FGH \sim \triangle FDE$ by AA similarity. Thus, $\frac{x}{x+17.8} = \frac{13.3}{13.3+10.7}$

Step2: Simplify denominator on right

Calculate the sum of the right-side denominator:
$13.3+10.7=24$
So the proportion becomes $\frac{x}{x+17.8} = \frac{13.3}{24}$

Step3: Cross-multiply to solve for $x$

$24x = 13.3(x+17.8)$
Expand the right side:
$24x = 13.3x + 13.3\times17.8$
Calculate $13.3\times17.8=236.74$

Step4: Isolate $x$ terms

Subtract $13.3x$ from both sides:
$24x - 13.3x = 236.74$
$10.7x = 236.74$

Step5: Solve for $x$

$x = \frac{236.74}{10.7}$

Answer:

22.1