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Question

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




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