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.

Question

Gillespie

Mathematics

8 August, 14:20

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.

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Answers (1)

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Madison · 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.