The sides of an equilateral triangle are (2a - b + 5), (a + b) and (2b - a + 2). What is the area of the triangle?
A
√34×a2
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B
√34×b2
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C
√34×49
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D
√34×81
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Solution
The correct option is C√34×49 ΔABC is an equilateral triangle. ⇒AB = BC = CA Now AB = BC gives 2b - a + 2 = a + b ⇒ b = 2a - 2 ....... (i) BC = CA gives a + b = 2a - b + 5 from(i) a + 2a - 2 = 2a - 2a + 2 + 5 ⇒ 3a = 9 ⇒ a = 3 ∴b = 2 (3) - 2 = 6 - 2 = 4 ∴AC = 2 (3) - 4 + 5 = 6 - 4 + 5 = 7 Area of equilateral Δ=√34(side)2 =√34(7)2 =√34×49