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Question

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 A a:b:c::3:5:7
Let the sides of triangle a,b,c which are in AP be xd,x,x+d
2s=3x
A=3534x2=3320x2 ....(1)
A2=3x2(x2+d)x2(x2d)
27400x4=34x2(x24d2)
x24d2=9100x2
d=2x5
sides are 3x5,x,7x5
a:b:c=3:5:7

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