Question

if a triangle has side lengths of 5.6 yards, 7.1 yards, and x yards, find the range of possible values of x. l

Answer 1

The answer is:

`1.5<x<12.7`

Explanation:

In order to determine the range of possible values, we have to know about the theorem of the triangle lengths.

The theorem is called "Triangle Inequality Theorem".This theorem states that the addition of the lengths of any 2 sides of a triangle must be greater than the third side.

I have attached an image that shows the inequalities of each side of a triangle.

So, in this case we have the values of two sides. Let be x the length value of the third side:

a=5.6

b=7.1

c=x

`a+b>x\\5.6+7.1>x\\12.7>x\\\\a+x>b\\5.6+x>7.1\\x>7.1-5.6\\x>1.5`

Finally, the range of possible values of x is:

`1.5<x<12.7`

Answer 2

Triangle has 3 sides.

1st side: 5.6 yards
2nd side: 7.1 yards
3rd side: x

7.1 yards - 5.6 yards = 1.5 yards
7.1 yards + 5.6 yards = 12.7 yards

x is between 1.5 yards and 12.7 yards.

1.5 < x < 12.7