Question

Tell whether a triangle can have sides with lengths 5, 11, and 7.

a) Acute triangle
b) Obtuse triangle
c) Right triangle
d) Not a valid triangle

Tell whether a triangle can have sides with lengths 1, 2, and 3.
a) Acute triangle
b) Obtuse triangle
c) Right triangle
d) Not a valid triangle

Answer 1

A triangle with sides 5, 11, and 7 is not a valid triangle. A triangle with sides 1, 2, and 3 is not a valid triangle either.

Step-by-step explanation:

A triangle can have sides with lengths 5, 11, and 7. To determine the type of triangle, we need to check the relationship between the square of each side:

1. 5^2 + 7^2 = 25 + 49 = 74
2. 11^2 + 7^2 = 121 + 49 = 170
3. 5^2 + 11^2 = 25 + 121 = 146

Since none of these calculations result in the square of one side being equal to or greater than the sum of the squares of the other two sides, this triangle is not a valid triangle.

The triangle with sides 1, 2, and 3 is also not a valid triangle because the sum of the lengths of the shorter two sides (1 + 2 = 3) is not greater than the length of the longest side (3).