Durante uma atividade de Matemática, professora Julieta distribuiu a cada um de seus alunos 4 canudinhos com medidas 2 cm, 3 cm, 7 cm e 8 cm. Nessa atividade, os alunos de Julieta tinham que construir triângulos com esses canudinhos, sem cortá-los. Quantos triângulos distintos cada um dos alunos de Julieta puderam formar com esses canudinhos?

Step-by-step explanation:

Given measures:

We see that:

Therefore we can't make triangles with the sides of 2 cm, 3 cm and 7 cm or 8 cm

Possible solutions are:

So we can make two different triangles

the polynomial is a perfect square trinomial of the form a^2-2ab+b^2:

option a. true

step-by-step explanation:

9x^2-12x+4

comparing with the form a^2-2ab+b^2

1.) a^2=9x^2

solving for a: square root both sides of the equation:

sqrt(a^2)=sqrt(9x^2)

a=sqrt(9) sqrt(x^2)

a=3x

2.) b^2=4

solving for b: square root both sides of the equation:

sqrt(b^2)=sqrt(4)

b=2

to be a perfet square trinomial 2ab must be equal to 12x. let's check:

2ab = 2 (3x) (2)

2ab = 12x

correct