Question

Please help!!

6a. Given two sides of 5 cm and 6 cm. To determine a triangle the MINIMUM whole number length of the third side would be _____ cm. *

6b. Given two sides of 5 cm and 6 cm. To determine a triangle the MAXIMUM whole number length of the third side would be _____ cm. *

7a. Given two sides of 3 cm and 7 cm. To determine a triangle the MINIMUM whole number length of the third side would be _____ cm. *

7b. Given two sides of 3 cm and 7 cm. To determine a triangle the MAXIMUM whole number length of the third side would be _____ cm. *

8a. Given two sides of 4 cm and 10 cm. To determine a triangle the MINIMUM whole number length of the third side would be _____ cm. *

8b. Given two sides of 4 cm and 10 cm. To determine a triangle the MAXIMUM whole number length of the third side would be _____ cm. *

9a. Given two sides of 1 cm and 12 cm. To determine a triangle, the MINIMUM whole number length of the third side would be _____ cm. *

9b. Given two sides of 1 cm and 12 cm. To determine a triangle, the MAXIMUM whole number length of the third side would be _____ cm. *

Answer 1

6a) 1

6b) 11

7a) 4

7b) 10

8a) 6

8b) 14

9a) 11

9b) 13

Explanation:

In order to make a triangle, we need to follow this property:

a <= b + c

(Known as "triangle inequality")

Where 'a' is the bigger side and 'b' and 'c' are the other two sides.

So, using this property, we can solve the following problems:

6a) Maximum side will be 6:

6 <= 5 + c

c = 1

6b) Minimum sides will be 5 and 6:

a <= 5 + 6

a = 11

7a) Maximum side will be 7:

7 <= 3 + c

c = 4

7b) Minimum sides will be 3 and 7:

a <= 3 + 7

a = 10

8a) Maximum side will be 10:

10 <= 4 + c

c = 6

8b) Minimum sides will be 4 and 10:

a <= 4 + 10

a = 14

9a) Maximum side will be 12:

12 <= 1 + c

c = 11

9b) Minimum sides will be 1 and 12:

a <= 1 + 12

a = 13