ദീർഘചതുരം ABCD യിൽ, 18 സെ.മീ2 വിസ്തീർണ്ണമുള്ള ഒരു സമപാർശ്വ ത്രികോണമാണ് ADE. കൂടാതെ, EC = 2 × DE. AD = DE ആണെങ്കിൽ, ABCD യുടെ വിസ്തീർണ്ണം എന്താണ്?

F1 S.C 6.2.20 Pallavi D3

  1. 72 സെ.മീ2
  2. 90 സെ.മീ2
  3. 108 സെ.മീ2
  4. 126 സെ.മീ2

Answer (Detailed Solution Below)

Option 3 : 108 സെ.മീ2
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⇒ ADE എന്നത് ഒരു സമപാർശ്വ ത്രികോണമാണ്, ഇവിടെ AD = DE = a

⇒ ADE യുടെ വിസ്തീർണ്ണം = 1/2 × AD × DE = 18 

∴ 1/2 × a2 = 18

⇒ a = 6 സെ.മീ.

⇒ AD = DE = 6 സെ.മീ 

⇒ EC = 2 × DE = 2 × 6 = 12 സെ.മീ 

 ∴ ABCD യുടെ വിസ്തീർണ്ണം= AD × DC = 6 × (DE + EC) = 6 × (6 + 12) = 108 സെ.മീ2
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