Question

The Dittany family's vegetable garden is shaped like a scalene triangle. Two of the sides measure 6 feet and 10 feet. Which could be the length of the third side, in feet?

Question 2 options:

18

16

9

6

Answer 1

The length of the third side could be 9 ft

Explanation:

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

so

In this problem

Let

c-----> the length of the third side, in feet

Applying the Triangle Inequality Theorem

1)
`6+10>c` ------->
`c<16\ ft`

2)
`c+6>10` ----->
`c>4\ ft`

so

The length of the third side must be greater than 4 ft and less than 16 ft

Remember that

The scalene triangle has three different sides

therefore

The length of the third side could be 9 ft