The sides of a Δ are in A.P. and its area is 35× (area of an equilateral triangle of the same perimeter). Find the ratio of its sides.
A
a:b:c::3:5:7
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B
a:b:c::4:5:7
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C
a:b:c::5:6:7
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D
None of these
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Solution
The correct option is Aa:b:c::3:5:7 Let the sides of triangle a,b,c which are in AP be x−d,x,x+d ⇒2s=3x ⇒A=35√34x2=3√320x2 ....(1) ⇒A2=3x2(x2+d)x2(x2−d) ⇒27400x4=34x2(x24−d2) ⇒x24−d2=9100x2 ⇒d=2x5 ⇒ sides are 3x5,x,7x5 ∴a:b:c=3:5:7