Question

On one banner, Sam wants to create triangles with side lengths of 9 inches and 2 inches. How many unique (one and only one) triangles with whole number side lengths can he make?

a) 0
b) 1
c) 2
d) 3

Answer 1

Using the Triangle Inequality Theorem, Sam can make 3 unique triangles with whole number side lengths when two of the sides are 9 inches and 2 inches.

Step-by-step explanation:

In mathematics and specifically in triangle geometry, the Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Since Sam wants to create triangles with two side lengths of 9 inches and 2 inches, the third side must be greater than 7 inches (9 - 2) and less than 11 inches (9 + 2) to satisfy this condition. Therefore, Sam can have side lengths of 8, 9, or 10 inches for the third side, each creating a unique triangle.

Thus, there are 3 unique triangles that Sam can make with whole number side lengths when two of the sides are 9 inches and 2 inches.