Question

(PLEASE HELP)

Which of the following would NOT work to make a triangle with the two slide lengths of 2 and 6

A.6
B.5
C.7
D.4

Answer 1

Given:

The two sides of a triangle are 2 and 6.

To find:

The side length that would NOT work to make a triangle with the two slide lengths of 2 and 6.

Solution:

For a triangle, the sum of two smaller sides must be greater than the largest side.

Let x be the third side.

Case 1: x is the largest side, then

`2+6>x`

`8>x` ...(i)

Case 2: x is not the largest side, then

`2+x>6`

`x>6-2`

`x>4` ...(ii)

From (i) and (ii), we get

`4<x<8`

Here, 4 and 8 are not included.

6, 5, 7 are included in the above interval, but 4 is not included in the above interval. It means 4 would NOT work to make a triangle with the two slide lengths of 2 and 6.

Therefore, the correct option is D.