Question

Question #5be91

Answer 1

Triangle with given sides is not possible.

Explanation:

In a triangle, the sum of any two sides must be greater than the third side.

Since the sum of first two sides is not greater than the third side, this triangle is not possible.

`a+b>c` `` must be true.

`10+20>30`

`30color(red)cancel{color(black)>}30`

Triangle with given sides is not possible.

Answer 2

No triangle with sides equal to given dimensions can be drawn. The Triangle Inequality Theorem states that Sum of two sides of a triangle must be greater than the length of third side.

Explanation:

On a side note general derivation for finding radius of incircle is given below.

Let `r` be radius of incircle with centre `O` of the triangle `ABC` as in the figure above.
Area of this triangle can be calculated in two ways.

1. Heron's Formula
2. Sum of areas `Deltas AOC,AOB and BOC`, using the formula Area of a `Delta=1/2"base"xx"height"`. We observe that with given sides as bases, height of all three triangles can be taken as radius of the incircle.

Equating area calculated in 1 and 2 will give us the value of `r`

.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.

The Triangle Inequality Theorem can be demonstrated as below in this case.

Area `ABC=sqrt(s(s-a)(s-b)(s-c))`, where `s=(a+b+c)/2`
Now `s=(10+20+30)/2=30`
`:.`Area `ABC=sqrt(30(30-10)(30-20)(30-30))=0`