Question

Does anyone know the answers to this, I had to do this yesterday but I didn´t know any of the questions.

Answer 1

(A)

(1) NO

(2) YES

(B)

(3) YES

(4) NO

(5) YES

Explanation:

According to the triangle sum theorem, the three interior angles of any triangle add up to 180 degrees. So, if we add up the three angles given, to be a triangle, they have to add up to 180 degrees.

38 + 42 + 110 = 190

So, ( (1) 38, 42, 110 ) is not a triangle becuase it adds up to more than 180 degrees (1).

20 + 40 + 120 = 180

So, ( (2) 38, 42, 110 ) is a triangle because it adds up to 180 degrees (2).

For the lengths for a triangle, the length of one side of a triangle must be greater than the difference and less than the sum of the lengths of the other two sides. This is saying:

A-B < C

A+B > C

So to find if they can be, simply plug in the values.

(3)

4-3 < 3

True : 1 < 3

4+3 > 3

True : 7 > 3

(3) is a triangle.

(4)

3-2 < 5

True : 1 < 5

3+2 > 5

False : 5 > 5

(4) is not a triangle

(5)

5-2.5 < 4

True : 2.5 < 4

5+2.5 > 4

True : 7.5 > 4

(5) is a triangle