Question

Pepe is putting up a fence in his backyard to enclose a garden in form of a triangle. The garden

already has sides enclosed with eight feet and five feet of fence, respectively. What can you say
about the length of the third side?
A
The side needs a fence that is shorter than 8 ft. but not necessarily longer than 5 ft.
The side needs a fence that is longer than 3 ft. and shorter than 13 ft.
C
The side needs exactly 8 ft. of fence.
The side needs exactly 11 ft. of fence.
D

Answer 1

We know that in a triangle, given two sides, the third one must be smaller than the sum of the given sides, but greater than their difference:

z < x + y

z > x - y

Therefore, the length of the third side will be between the difference and the sum of the other two sides. In our case:

x + y = 13

x - y = 3

Hence, the correct answer is: B) The side needs a fence that is longer than 3ft. and shorter than 13ft.

Explanation: