Triangle Similarity Calculation
We are given that triangle ABC is similar to triangle EDF, denoted as \(\Delta ABC \sim \Delta EDF\). This similarity means that the ratio of their corresponding sides is constant.
The proportion of corresponding sides is:
\( \frac{AB}{ED} = \frac{AC}{EF} = \frac{BC}{DF} \)
Given Side Lengths:
- \(AB = 5 \text{ cm}\)
- \(AC = 7.5 \text{ cm}\)
- \(DF = 15 \text{ cm}\)
- \(ED = 12.5 \text{ cm}\)
Finding Remaining Sides:
First, determine the ratio of similarity using the known corresponding sides, AB and ED:
Ratio \(k = \frac{AB}{ED} = \frac{5}{12.5} = 0.4\)
This ratio \(k=0.4\) applies to all corresponding sides.
Calculating Side BC:
Use the similarity proportion \(\frac{AB}{ED} = \frac{BC}{DF}\):
\( \frac{5}{12.5} = \frac{BC}{15} \)
Solve for BC:
\( BC = 15 \times \frac{5}{12.5} = 15 \times 0.4 \)
\( BC = 6 \text{ cm} \)
Calculating Side EF:
Use the similarity proportion \(\frac{AB}{ED} = \frac{AC}{EF}\):
\( \frac{5}{12.5} = \frac{7.5}{EF} \)
Solve for EF:
\( EF = 7.5 \times \frac{12.5}{5} = 7.5 \times 2.5 \)
\( EF = 18.75 \text{ cm} \)
Sum of Remaining Sides:
The remaining sides of the two triangles are BC (from \(\Delta ABC\)) and EF (from \(\Delta EDF\)).
Calculate their sum:
Sum \(= BC + EF = 6 \text{ cm} + 18.75 \text{ cm}\)
Sum \(= 24.75 \text{ cm}\)
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