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Alice plans to put her dog on 20foot leash in her fence in backyard. She will temporary attach the leash to the back of her rectangle shaped home which is centered in the lot.
A) Alice is considering two places to attach the leash to the back wall of her house these two places are labeled X and Y in the diagram. Point X is at the corner of the house. Point X is at the corner of the house. Point Y is 20 feet from corner X. The dimensions of her house are 50 feet by 100 feet. How many square feet of yard space are available to the dog if the dog is tied to the leash is at attached at point X?
B) Which of the two positions X or Y provides the greater area for the dog to walk? Show all calculations to explain your answer.
C) Alice buy a new 35 foot leash and decides to attach it to a corner of the fence in the backyard at point Z. Will the placement of the new 35 foot leash provide more square feet of yard space for the dog than the placement of the 20 foot leash at either point X or Point Y? The dog is unable to jump the fence
A) pi*r^2 - 1/4 of the circle.
B) A is better because the dong only gets half of a 20r circle rather than 3/4's of one
c) calculate what 1/4 of a 35r circle is and compare it to the answer you got for A
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How do i do that?
area of a circle is pi*r^2 you know the r is 20ft because thats the length of the leash. so figure out the total and then divide by 4 and then you have one quarter. total minus one quarter (the house is a 90 degree angle so its exactly one quarter of the circle missing) gets you the area the dog has to run. C is just like A but with a new radius and you use only the quarter part