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 8ft. but not necessarily longer than 5ft. B. The side needs a fance that is longer than 3ft. and shorter than 13ft. C. The side needs exactly 8ft. of fence. D.. The side needs exactly 11ft. of fence.

Answer 1

The side needs a fence that is longer than 3 ft. and shorter than 13 ft.

Explanation:

We are given backyard to enclose a garden in form of a triangle.

First side 'x' = 8 feet.

Second side 'y' = 5 feet

Third side = z

Property of triangle : the third side must be smaller than the sum of the other two sides but greater than their difference

`\Rightarrow z<x+y`

`\Rightarrow z<8+5`

`\Rightarrow z<13`

So, third side must be shorter than 13 feet

`\Rightarrow z>x+y`

`\Rightarrow z>8-5`

`\Rightarrow z>3`

So, third side must be longer than 3 feet

Hence option B is correct :The side needs a fence that is longer than 3 ft. and shorter than 13 ft.

Answer 2

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.