Question

In the invoice that specifies the side lengths of the triangular sail as 7.5 meters, 4.8 meters, and 2.5 meters, suppose the mistake was in the length of 2.5 meters. Determine the range of values that are possible for the third side length, x, of the sail.

Answer 1

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. Apply this theorem to the sail length measurements: 7.5 meters, 4.8 meters, and x meters.

First assume x is the longest side, and then assume x as the shortest side. We get these inequalities:

7.5 + 4.8 > x

4.8 + x > 7.5

Simplify each inequality:

x < 12.3; x > 2.7

Therefore, the range of the possible values of x is 2.7 < x < 12.3. The third side length of the sail must be greater than 2.7 meters but less than 12.3 meters.

Explanation:

Answer 2

2.7 < x < 12.3 meters

Explanation:

You want to know the possible lengths of the third side of a triangle, given that two sides are 7.5 m and 4.8 m.

Triangle inequality

The triangle inequality requires the sides of a triangle have the relationship ...

a + b > c

for any assignment of side lengths to the letters a, b, c. In effect, this means the length of a third side must lie between the sum and the difference of the other two sides.

7.5 -4.8 < x < 7.5 +4.8

2.7 < x < 12.3 . . . . . meters