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The ratio of the areas of two similar triangles ∆ABC and ∆DEF is 9 ∶ 16. If the length of AB = 9 cm, find the length of DE.
- A8 cm
- B12 cm
- C16 cm
- D20 cm
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CCommunity
As we know, the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides
Considering similar triangles ?ABC and ?DEF, we have,
⇒ Area(?ABC)/Area(?DEF) = (AB/DE)2
⇒ 9/16 = (9/DE)2
⇒ √(9/16) = 9\DE
⇒ 3/4 = 9/DE
∴ DE = 9 × (4/3) = 12 cm
Considering similar triangles ?ABC and ?DEF, we have,
⇒ Area(?ABC)/Area(?DEF) = (AB/DE)2
⇒ 9/16 = (9/DE)2
⇒ √(9/16) = 9\DE
⇒ 3/4 = 9/DE
∴ DE = 9 × (4/3) = 12 cm