If A is the area and 2s the sum of the s...

If A is the area and 2s the sum of the sides of a triangle,then

`Ale (s^2)/(4)`

`Ale(s^2)/(3sqrt(3))`

`Alt (s^2)/(sqrt(3)`

none of these

Text Solution

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The correct Answer is:

A, B

We have
`2s = a + b + c`
`A^(2) = s (s - a) (s - b)(s - c)`
Now,
`A.M. ge G.M`
`implies (s + (s - a) + (s - b) + (s - c))/(4) ge [s(s-a)(s-b)(s-c)]^(1//4)`
`implies (4s - 2s)/(4) ge [A^(2)]^(1//4)`
`implies s//2 ge A^(1//2)` or `A le s^(2)//4`
Also,
`((s - a) + (s - b) + (s - c))/(3) ge [(s - a) (s - b) (s - c)]^(1//3)`
`implies (s)/(3) ge [(A^(2))/(s)]^(1//3)`
or `(A^(2))/(s) le (s^(3))/(27)`
or `A le (s^(2))/(3sqrt(3))`

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If A is the area and 2s is the sum of the sides of a triangle, then

`A le (s^(2))/(4)`

`A le (s^(2))/(3sqrt3)`

`A lt (s^(2))/(sqrt3)`

none of these

If Delta denotes area of triangle and P denotes the sum of the 3 sides of triangle then

`Delta=(P^(2))/(4)`

`Deltale(P^(2))/(12sqrt(3))`

`Deltagt(P^(2))/(6sqrt(3))`

None of these

In a triangle the sum of lengths of two sides sides x and the product of the lengths of the saem two sides is y. if x^(2)-c^(2)=y , where c is the length of the third side of then triangle, then the circumradius of the triangle is

`(c)/(3)`

`(c)/(sqrt(3))`

`(3)/(2)y`

`(y)/(sqrt(3))`