A landscape architect submitted a design for a triangle-shaped flower garden with side lengths of 21 feet, 37 feet, and 15 feet to a customer. Explain why the architect was not hired to create the flower garden.
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He was not hired because 15+21<37
The landscape architect was not hired to create the flower garden because the submitted design violates the basic property of triangles, known as the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, the architect's design has side lengths of 21 feet, 37 feet, and 15 feet. To determine if it forms a valid triangle, we can check if the sum of the two shorter sides is greater than the longest side.
Let's calculate the sums:
21 + 15 = 36
37 + 15 = 52
21 + 37 = 58
As we can see, none of the sums (36, 52, and 58) are greater than the remaining side's length. Since the triangle inequality theorem is violated, the design cannot form a valid triangle. Therefore, the architect was not hired to create the flower garden.
Because the given side lengths of the triangle do not follow the triangle inequality theorem.
The theorem states that the sum of any sidelengths of the triangle is greater than the length of the third side.
In this case, 21 + 15 is not greater than 37.