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.
The architect was not hired because those side lengths are impossible to construct a triangle. Imagine the 2nd piece, 37 ft. Now, take the other two sides: 15 and 21 ft. The two shorter pieces would be, when added together, shorter than the first piece alone (21+15<37). It is not possible to construct a triangle given those side lengths.
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The architect was not hired to create the flower garden because the submitted design does not meet the requirements or expectations of the customer. The customer might have had specific preferences or criteria that the architect failed to address in the design.
To determine why the design does not meet the requirements, we need to analyze the properties of the triangle formed by the given side lengths (21 feet, 37 feet, and 15 feet). We can use the triangle inequality theorem to determine if the triangle is possible or not.
According to the triangle inequality theorem, for any triangle with side lengths a, b, and c, the sum of the lengths of any two sides must always be greater than the length of the third side.
If we apply this theorem to the given side lengths, we can check if they satisfy the triangle inequality:
21 + 37 = 58 (Sum of the two shorter sides)
15 (Length of the longest side)
Since 58 is not greater than 15, the given side lengths do not satisfy the triangle inequality theorem. Therefore, it is impossible to create a triangle with side lengths of 21 feet, 37 feet, and 15 feet.
Based on this analysis, the architect's design was not hired because it did not meet the basic requirement of successfully creating a triangle with the given side lengths. The customer might have expected a different design or might have preferred a more well-designed and feasible flower garden.