Makayla wants to classify the triangle below. Select all of the terms that apply. (1 point) Responses acute acute isosceles isosceles obtuse obtuse right right scalene scalene 5cm 5cm 7.1 cm

Answer 1

To classify the triangle with side lengths of 5 cm, 5 cm, and 7.1 cm, we can consider the following:

1. Type by sides:

   • The triangle has two sides of the same length (5 cm and 5 cm) and one side of a different length (7.1 cm). This makes it an isosceles triangle.

2. Type by angles:

   • To determine if it is acute, obtuse, or right, we can use the triangle inequality theorem and the Pythagorean theorem.
   • The lengths of the sides are \( a = 5 \), \( b = 5 \), and \( c = 7.1 \) (where \( c \) is the longest side).
   • For it to be a right triangle, we check if \( c^2 = a^2 + b^2 \): \[ 7.1^2 \approx 50.41 \] \[ 5^2 + 5^2 = 25 + 25 = 50 \] Since \( 50.41 > 50 \), this triangle is not a right triangle.
   • To check if it is obtuse, we need \( c^2 > a^2 + b^2 \) (which we already established holds true).
   • Therefore, this triangle is an obtuse triangle.

Based on this classification, the terms that apply to the triangle are:

• isosceles
• obtuse

Answer 2

I know it has a right degree angle

Answer 3

If there is a right angle in the triangle, then the triangle is classified as a right triangle. Given the side lengths you provided (5 cm, 5 cm, and 7.1 cm), we can verify if it indeed contains a right angle.

For a triangle to be a right triangle, it must satisfy the Pythagorean theorem, which states:

\[ c^2 = a^2 + b^2 \]

where \( c \) is the length of the longest side.

Given:

• \( a = 5 \) cm
• \( b = 5 \) cm
• \( c = 7.1 \) cm

Let's check if it fulfills the condition for being a right triangle:

1. Calculate \( c^2 \):

   • \( (7.1)^2 = 50.41 \)

2. Calculate \( a^2 + b^2 \):

   • \( 5^2 + 5^2 = 25 + 25 = 50 \)

Now, check if \( c^2 \) equals \( a^2 + b^2 \):

• \( 50.41 \neq 50 \)

Since \( 50.41 \) is not equal to \( 50 \), the triangle does not satisfy the condition for a right triangle.

Thus, despite having a right angle, the side lengths you provided do not create a triangle with a right angle. If you have different measures or if there is additional context, please provide that, and I can reassess! If there is clarification regarding the triangle's classification with specific degrees, please let me know!