Question

A teacher draws a triangle on the board and assigns the measures of respective side lengths as 2cm, 3cm and 5cm. A student argues that we cannot form a triangle with these measures. As a prospective teacher, whom do you side with? The teacher or the student? Explain in not more than five lines

Answer 1

As a prospective teacher,I will be in the student's side.

• According,to the theorem of "Triangle Inequality", the sum of the any two sides of a triangle will be greater than the third side of that triangle.

• Let,the three sides of the given triangle A,B and C, respectively. So,

A = 2 cm

B = 3 cm

C = 5 cm

• Now, according to theorem of "Triangle Inequality",the A+B will be greater than C.

• But,here A+B = 2+3 = 5 cm

And,C = 5 cm

So in this case,A+B = C

• In this way,the given measurements do not satisfy the "Triangle Inequality" theorem,and the triangle is impossible. So,the student is correct.