Two sides of a triangle measure 4 inches and 9 inches. Determine which cannot be the perimeter of the triangle. A.19 inches, B.21 inches, C.28 inches, D.26 inches
To determine which cannot be the perimeter of the triangle, we first need to apply the triangle inequality theorem. According to the theorem, the sum of the lengths of any two sides of a triangle must always be greater than the length of the third side.
Let's check each answer choice:
A. 19 inches: To form a triangle, the sum of the two smaller sides should be greater than the longest side. But if we add the two given sides (4 and 9 inches), the total is 13 inches, which is greater than 19 inches. So 19 inches can be the perimeter of the triangle.
B. 21 inches: Following the same process, if we add the two given sides (4 and 9 inches), the total is 13 inches, which is less than 21 inches. Therefore, 21 inches cannot be the perimeter of the triangle.
C. 28 inches: Adding the two given sides (4 and 9 inches) results in 13 inches, which is less than 28 inches. Hence, 28 inches cannot be the perimeter of the triangle.
D. 26 inches: Once again, adding the two given sides (4 and 9 inches) equals 13 inches, which is less than 26 inches. Therefore, 26 inches cannot be the perimeter of the triangle.
So, the answer is B. 21 inches, which cannot be the perimeter of the triangle.