The sum of n A.M.'s between two numbers is 20. If the last mean is double of the first and one number is three times the other,
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The perimeter = 20 and AC = 8
Now as it is not mentioned which sides are equal of the isosceles triangle ABC,
We have two possible situations.
1)
If AC is the base
In that case AB = BC
Now AC = 8, AB = x , BC = x
So x + x + 8 = 20
2x + 8 = 20
2x = 12
x = 6
AB = BC = 6
2)
IF AC is not the base,
Then
AC = BC or AC = AB
So BC = 8 or AB = 8
If AB = AC = 8
Then
BC + 8 + 8 = 20
BC = 4
So there are two possible lengths of BC
Either it is BC = 8 or BC = 6 or BC = 4
The figure is attached for your reference.
