Two sides of a triangle measure 7 cm and 15 cm . Which of the following could not be the length of the third side ?
A. 5 cm
B. 9 cm
C. 15 cm
D. 22 cm
I'm confused because at first I tried Pythagorean thereom and it didn't really work .
7+15=22
7-15=-8
the line has to be between 8 and 22 to work, otherwise it would be a straight line so it cannot be a, 5cm
To determine which of the given lengths could not be the length of the third side of the triangle, we can apply the triangle inequality theorem.
According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's check each option:
A. 5 cm:
7 cm + 5 cm = 12 cm (less than 15 cm)
15 cm + 5 cm = 20 cm (greater than 7 cm)
Therefore, it is possible for the third side to be 5 cm.
B. 9 cm:
7 cm + 9 cm = 16 cm (greater than 15 cm)
15 cm + 9 cm = 24 cm (greater than 7 cm)
Therefore, it is possible for the third side to be 9 cm.
C. 15 cm:
The triangle inequality theorem states that the sum of the lengths of any two sides must be greater than the length of the third side. In this case, the sum of the two given sides is already equal to 15 cm. Therefore, it is not possible for the third side to be 15 cm.
D. 22 cm:
7 cm + 22 cm = 29 cm (greater than 15 cm)
15 cm + 22 cm = 37 cm (greater than 7 cm)
Therefore, it is possible for the third side to be 22 cm.
Based on the triangle inequality theorem, the length of the third side cannot be 15 cm, so the answer is C.
To determine which length could not be the length of the third side of the triangle, we can use the triangle inequality theorem.
According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's test each option using the given lengths of the triangle sides:
A. 5 cm: 7 cm + 5 cm = 12 cm (Not greater than 15 cm) - This could not be the length of the third side.
B. 9 cm: 7 cm + 9 cm = 16 cm (Greater than 15 cm) - This could be the length of the third side.
C. 15 cm: 7 cm + 15 cm = 22 cm (Equal to 22 cm) - This could be the length of the third side.
D. 22 cm: 7 cm + 22 cm = 29 cm (Greater than 15 cm) - This could be the length of the third side.
Therefore, the answer is Option A. 5 cm could not be the length of the third side since the sum of the two given lengths (7 cm and 5 cm) is not greater than the length of the remaining side (15 cm).