Question

solve for x. round your answer to the nearest tenth if necessary.

triangle diagram with points d, e, b, f, c; de=10, eb=5, fc=10, df=x

answer attempt 1 out of 2
x = blank submit answer

Explanation:

Step1: Identify Similar Triangles

Since \( EF \parallel BC \), triangles \( DEF \) and \( DBC \) are similar by the Basic Proportionality Theorem (Thales' theorem).

Step2: Set Up Proportion

The ratio of corresponding sides in similar triangles is equal. So, \(\frac{DE}{DB}=\frac{DF}{DC}\). We know \( DE = 10 \), \( EB = 5 \), so \( DB=DE + EB=10 + 5 = 15 \), and \( DC=DF + FC=x + 10 \). Substituting the values, we get \(\frac{10}{15}=\frac{x}{x + 10}\).

Step3: Solve the Proportion

Cross - multiply: \(10(x + 10)=15x\).
Expand: \(10x+100 = 15x\).
Subtract \(10x\) from both sides: \(100=15x - 10x\).
Simplify: \(100 = 5x\).
Divide both sides by 5: \(x=\frac{100}{5}=20\).

Answer:

\(x = 20\)