Question
Triangle ABC is similar to triangle DEF. For triangle
ABC, sides are AB = 6 cm, BC = 8 cm, CA = 10 cm. If DE corresponds to AB and DE = 9 cm, find the lengths of EF and FD and the area of triangle DEF.Solution
Scale factor (DEF to ABC): k = DE / AB = 9 / 6 = 3/2 So: EF corresponds to BC ⇒ EF = k × BC = (3/2) × 8 = 12 cm FD corresponds to CA ⇒ FD = k × CA = (3/2) × 10 = 15 cm Area of triangle ABC: Right-angled at B (6-8-10 triangle): Area(ABC) = (1/2) × 6 × 8 = 24 cm² Area scales with square of linear factor: Area(DEF) = k² × Area(ABC) = (3/2)² × 24 = (9/4) × 24 = 54 cm²
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