Question

question 4
part a
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.

Explanation:

State the Triangle Inequality Theorem

$$ a + b > c $$

Apply the theorem to the given side lengths

$$
LATEXBLOCK0
$$

Determine the contradiction

$$ 7.3 gtr 7.5 $$

Answer:

According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be strictly greater than the length of the remaining side.

For the given measurements of \(2.5\text{ m}\), \(4.8\text{ m}\), and \(7.5\text{ m}\):

$$2.5 + 4.8 = 7.3\text{ m}$$

Since \(7.3\text{ m} < 7.5\text{ m}\), the sum of the two shorter sides is less than the longest side, making it impossible to form a closed triangular sail.