Question

10. Error Analysis A student draws a triangle with a perimeter 36 cm. The

student says that the longest side measures 18 cm. How do you know that the
student is incorrect? Explain.​

Answer 1

see the explanation

Explanation:

we know that

The Triangle Inequality Theorem 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