Question

At the beginning of the lesson, Jacob determined that there was a problem with the sail length measurements of 7.5 meters, 4.8 meters, and 2.5 meters. Explain how Jacob was able to determine there was a problem with the specifications of the triangular 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. So, apply this theorem to the sail length measurements 7.5 meters, 4.8 meters, and 2.5 meters:

7.5 + 4.8 > 2.5

7.5 + 2.5 > 4.8

4.8 + 2.5 IS NOT GREATER THAN 7.5

Notice that the last inequality is not true, so the triangle inequality theorem fails. In this case, the sum of two lengths of the sail is less than the length of the third side length. Therefore, it’s not possible to build a triangular sail with the length specifications of 7.5 meters, 4.8 meters, and 2.5 meters.

Explanation:

Answer 2

Jacob was able to determine there was a problem with the specifications of the triangular sail because of the Pythagorean theorem.

Explanation:

Assume the triangular sail is a right triangle.

The Pythagorean theorem says:
`A^(2) + B^(2) = C^(2)`

If A = 4.8, B = 2.5, and C = 7.5, then
`4.8^(2) + 2.5^(2) = 7.5^(2)`.

`4.8^(2) + 2.5^(2) = 23.04 + 6.25 = 29.29`

`7.5^(2) = 56.25`

In conclusion,
`29.29 \\eq 56.25`, so there is a problem with the sail.