A goat is tied to a shed with a barn next to it.

Question

A rectangular shed measuring 4 feet by 5 feet is located along the side of a barn. The barn is 20 feet wide and 45 feet long. A 3 year old goat is tethered to a corner of the shed, not against the barn, with an 8 foot rope. What is the possible amount of space that the goat would have to roam? Express your answer in inequality notation.

Someone help please im so confused. This is word by word. I did research and I found stuff like this but similar, not like this.

Is there a picture? It seems like the answer would be different depending on exactly how the barn and shed are aligned, and which corner the goat is tethered to. — Jair Taylor, Nov 02 '18 at 02:18
Where did you find this problem? Clearly, us math people have been missing out on the goat-age model of geometry — Sambo, Nov 02 '18 at 02:41
Sambo, my teacher gave it to me to see if we could do it. 9th grade. — Binzel, Nov 02 '18 at 02:54
I don’t think this qualifies as a duplicate. The barn, which isn’t in the other question, causes somewhat different geometry and arithmetic. — David K, Nov 02 '18 at 03:41
I don't think you need a picture for this because we are asked to find an upper bound on the area. I suspect we are supposed to figure out where we are to place the shed. @Binzel I salute you and your classmates. If my 9th grade teacher gave me this problem I would still be there. — John Douma, Nov 02 '18 at 04:52

Phil H · Answer 1 · 2018-11-02T20:38:43.077

0

Here are two possible solutions for my chosen configurations.

edited Nov 02 '18 at 20:38

answered Nov 02 '18 at 03:16

Phil H

5,689

If the shed is near the end of the barn wall the area can be larger. (As you say, “one possible solution.”) – David K Nov 02 '18 at 03:37
@David K Yes, hence my saying that this is one possible solution. – Phil H Nov 02 '18 at 03:42
Question, what is the circle with the 3 inside it? Otherwise I get everything else. – Binzel Nov 02 '18 at 03:45
@Binzel the rope is 8ft long, the side of the shed 5 ft, so the goat is able to circle the left corner at a radius of 8 - 5 = 3ft. – Phil H Nov 02 '18 at 03:48
@PhilH And about the "Inequality Notation"? It said express your answer in inequality notation. – Binzel Nov 02 '18 at 04:33
@Binzel Your guess is as good as mine but $138.211 < 44\pi$ by a tiny amount. – Phil H Nov 02 '18 at 05:09
@PhilH I think the answer should be $roamed~area~\le~188~ft^2$.As the question is now closed so.I am not able to upload my answer. – Rakibul Islam Prince Nov 02 '18 at 10:41
@Rakibul Islam Prince Too bad, what relative positions of the 2 structures did you use? Also, the question said to be a duplicate is different from this question. – Phil H Nov 02 '18 at 13:29
i am not able to post my answer – Rakibul Islam Prince Nov 02 '18 at 18:38

A goat is tied to a shed with a barn next to it.

1 Answers1