Using the side-splitter theorem, Daniel wrote a proportion for the segments formed by line segment DE. What is [tex]EC[/tex]?
[tex]\frac{BD}{DA}=\frac{BE}{EC} \\ \frac{5}{3}=\frac{4}{EC}[/tex]
A. 2 units
B. 2.4 units
C. 3 units
D. 3.75 units
Answer (2)
Using the side-splitter theorem, we found that EC equals 2.4 units by setting up a proportion and solving for the unknown length. The calculations showed that by cross-multiplying and isolating EC, we arrived at the final answer. Thus, the correct option is B. 2.4 units.
;
We are given the proportion 3 5 = EC 4 .
Cross-multiply to get 5 EC = 12 .
Divide by 5 to find EC = 5 12 .
The length of EC is 2.4 units.
Explanation
Analyze the problem and given data We are given the proportion D A B D = EC BE and the values B D = 5 , D A = 3 , and BE = 4 . We need to find the length of EC . The given equation is 3 5 = EC 4 .
Cross-multiply To solve for EC , we can cross-multiply: 5 \t \t × EC = 3 \t \t × 4
Simplify the equation This simplifies to: 5 EC = 12
Isolate EC Now, divide both sides by 5 to isolate EC : EC = 5 12
Calculate the value of EC Calculating the value: EC = 2.4
State the final answer Therefore, the length of EC is 2.4 units.
Examples
The side-splitter theorem is useful in architecture and construction when dividing spaces proportionally. For example, if you have a triangular plot of land and need to divide one side into specific ratios to allocate space for different structures, the side-splitter theorem helps determine the corresponding divisions on the other side, ensuring accurate and proportional space allocation.
