Question

solve for x. round your answer to the nearest tenth if necessary.
f
3·3
x
g
h
1·7
2
d
e
answer attempt 1 out of 2
x =
submit answer

Explanation:

Step1: Identify Similar Triangles

Since \( GH \parallel DE \), triangles \( FGH \) and \( FDE \) are similar by the Basic Proportionality Theorem (Thales' theorem). So, the ratios of corresponding sides are equal: \(\frac{FG}{FD}=\frac{FH}{FE}\).

Step2: Define Side Lengths

\( FG = 3.3 \), \( GD = 1.7 \), so \( FD = FG + GD = 3.3 + 1.7 = 5 \). Let \( FH = x \), \( HE = 2 \), so \( FE = x + 2 \).

Step3: Set Up Proportion

Substitute into the proportion: \(\frac{3.3}{5}=\frac{x}{x + 2}\).

Step4: Cross - Multiply and Solve

Cross - multiply: \( 3.3(x + 2)=5x \).
Expand: \( 3.3x+6.6 = 5x \).
Subtract \( 3.3x \) from both sides: \( 6.6 = 5x - 3.3x \).
Simplify: \( 6.6 = 1.7x \).
Solve for \( x \): \( x=\frac{6.6}{1.7}\approx3.9 \).

Answer:

\( x\approx3.9 \)