Question

in the diagram, segment ef is parallel to segment bc. df = 5.6, eb = 5.3, and fc = 4.4. find the length of segment de. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Apply Basic Proportionality Theorem

When a line is parallel to one side of a triangle and intersects the other two sides, it divides those sides proportionally. So:
$$\frac{DE}{EB} = \frac{DF}{FC}$$

Step2: Substitute given values

Plug in $DF=5.6$, $EB=5.3$, $FC=4.4$:
$$\frac{DE}{5.3} = \frac{5.6}{4.4}$$

Step3: Solve for DE

Multiply both sides by 5.3 to isolate DE:
$$DE = \frac{5.6 \times 5.3}{4.4}$$
Calculate the numerator first: $5.6 \times 5.3 = 29.68$
Then divide: $DE = \frac{29.68}{4.4} \approx 6.7$

Answer:

6.7