A study draws triangle with a perimeter 36cm.the study says that the longest side measures 18cm. how do you know that the student is incorrect?
Perimeter = 36
36 - 18 longest side = 18
This would mean that the remaining TWO sides total 18.
The length of any side of a triangle will always be less than the sum of the lengths of the other two sides and greater than the difference of the lengths of the other two sides.
18 is not less than sum of the other two
sides.
Well, it seems like the student might be doing some extra-curricular stretching with those numbers! If the longest side of a triangle measures 18cm, there's no way the perimeter can be 36cm. It's time for that student to take a math break and go back to the drawing board!
To determine if the student is incorrect, we can use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must always be greater than the length of the third side.
In this case, the student claims that the longest side measures 18 cm. Let's assume this is true. Then, based on the triangle inequality theorem, the sum of the lengths of the other two sides must be greater than 18 cm.
Using the given information, we know that the perimeter of the triangle is 36 cm. The perimeter is the sum of the lengths of all three sides. So, if the longest side is 18 cm, then the sum of the lengths of the other two sides must be 36 cm - 18 cm = 18 cm.
However, this is where the contradiction arises. The student claims that the longest side measures 18 cm, but the sum of the lengths of the other two sides (which would be equal to 18 cm) is not greater than 18 cm. This violates the triangle inequality theorem.
Therefore, based on this reasoning, we can conclude that the student's claim is incorrect.
To determine if the student is incorrect, we need to verify if the given information is consistent. Let's use the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
According to the student, the perimeter of the triangle is 36 cm, and the longest side measures 18 cm. Let's assume that the other two sides are x and y, where x is shorter than or equal to y.
The Triangle Inequality Theorem implies the following conditions:
1. x + y > 18 cm (the longest side)
2. y + 18 cm > x (the shorter side)
Now, let's consider these conditions and test them with the given information:
1. x + y > 18 cm
Since x + y must be greater than 18 cm, if we assume x = 0 cm, then y would need to be greater than 18 cm to satisfy this condition. However, this contradicts the fact that the perimeter of the triangle is 36 cm. Therefore, the condition is violated.
Hence, based on the Triangle Inequality Theorem, we can conclude that the student is incorrect in stating that the longest side measures 18 cm, as it would not be consistent with the given perimeter of 36 cm.