ABC and DEF are similar triangles. If the ratio of side AB to side DE is (andradic;2 + 1) andradic;3, then the ratio of the area of triangle ABC to that of the triangle DEF isa)(3 andndash; 2andradic;2) 3b)(9 andndash; 6andradic;2) 2c)1 (9 andndash; 6andradic;2)d)(3 + 2andradic;2) 2Correct answer is option 'C'. Can you explain this answer?

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ABC and DEF are similar triangles. If the ratio of side AB to side DE is (√2 + 1) ∶ √3, then the ratio of the area of triangle ABC to that of the triangle DEF is

a)
(3 – 2√2) ∶ 3
b)
(9 – 6√2) ∶ 2
c)
1 ∶ (9 – 6√2)
d)
(3 + 2√2) ∶ 2

Correct answer is option 'C'. Can you explain this answer?

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ABC and DEF are similar triangles. If the ratio of side AB to side DE ...

Area (ABC)/Area (DEF) = (AB/DE)² [ ∵ ABC ∼ DEF]
⇒ [(√2 + 1) /√3]²
⇒ [(2 + 1 + 2√2) /3]
⇒ [(3 + 2√2) /3]
⇒ (3 + 2√2) × (3 – 2√2) = 3² – (2√2)² = 9 – 8 = 1
⇒ (3 + 2√2) = 1/(3 – 2√2)
⇒ [(3 + 2√2) /3] = 1/[(3 – 2√2) × 3]
⇒ 1/(9 – 6√2)
∴ AB ∶ DE = 1 ∶ (9 – 6√2)

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ABC and DEF are similar triangles. If the ratio of side AB to side DE is (√2 + 1) ∶ √3, then the ratio of the area of triangle ABC to that of the triangle DEF isa)(3 – 2√2) ∶ 3b)(9 – 6√2) ∶ 2c)1 ∶ (9 – 6√2)d)(3 + 2√2) ∶ 2Correct answer is option 'C'. Can you explain this answer?

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