Answer:
see the explanation
Step-by-step explanation:
we know that
The <u>Triangle Inequality Theorem</u> states that the sum of any 2 sides of a triangle must be greater than the measure of the third side
In this problem
If the perimeter of triangle is equal to 36 cm
The longest side can't be equal to 18 cm
The student is incorrect
Because if the longest side is equal to 18 cm, and the perimeter is equal to 36 cm, then the sum of the other two sides is equal to 18 cm
and
Applying the triangle inequality theorem
Let
c -----> the longest side
a and b the other two sides
we have that
if c=18 cm
a+b > c
a+b > 18 cm
therefore
If the longest side is 18 cm, the sum of the other two sides must be greater than 18 cm and the perimeter will be greater than 36 cm
