Question

Which measurements could create more than one triangle?

A) a triangle with sides measuring 9 inches, 12 inches, and 15 inches
B) a triangle with angles measuring 60°, 70°, and 80°
C) a right triangle with acute angles measuring 20° and 70°
D) a triangle with sides measuring 20 cm and 35 cm and an included angle measuring 45°

Answer 1

In order to form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Option A and D satisfy this condition and can create triangles.

Step-by-step explanation:

In order to create a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Using this rule, we can analyze each option:

A) 9 + 12 = 21, which is greater than 15, so it can form a triangle.

B) The sum of the angles is 60° + 70° + 80° = 210°, which is greater than 180°, so it cannot form a triangle.

C) The sum of the angles is 20° + 70° = 90°, which is less than 180°, so it cannot form a triangle.

D) Since two sides are given and one angle is given, we can use the Law of Cosines to check if it can form a triangle. By using the formula c^2 = a^2 + b^2 - 2ab*cos(C), where c is the side opposite the angle C, a = 20 cm, b = 35 cm, and C = 45°, we can calculate that c^2 = 1125 cm^2. Since the square of a length cannot be negative, it can form a triangle.