Find the area on the lawn on which the goat can graze.

[gen_shao]

A lawn ABC is in the form of a right triangle whose leg AC =120m and a short leg BC = 60m. A goat is tied to a peg D which is located outside the triangle and is 25m from BC and 115m from AC. The farthest distance its mouth can reach is 65m from the peg. Find the area on the lawn on which the goat can graze.

a.) 3152.44 b.) 1352.44 c.)2135.44 d.) 4135.24

the correct answer is supposedly letter a.
this is frustrating because the area that i solved is less than a thousand and not even within the choices..

it seems that i cant find the correct placement of the peg that would yield an area of 3152.44

btw... all areas on the choices are in m^2

please help ...thanks

 

[gen_shao]

Unless a diagram is provided, no can do.
Something is missing...

http://mymathforum.com/geometry/257384-find-area-lawn-goat-can-graze.html#post447100

I think it should look like this..... please find the area...... TY

 

[ksdhart]

Now, correct me if I'm wrong here, because Geometry is definitely not my area of expertise, but it seems this problem, as written, is literally unsolvable. We're told the peg is 115m from the leg AC. I believe the set of all points k units from a line form two parallel lines k units away . For simplicity's sake, let's say AC runs from (0,0) to (0,120). So any point 115m from AC would be lie on one of the two lines x = +/- 115. The points A, B, and C form a triangle, so the leg BC runs from (0,120) to (60,120). Any point 25m from BC would lie on the either the line y = 95 or y = 145. And by graphing this out, I come to the conclusion that no point can ever be both 115m from AC and 25m from BC. Since there are no valid positions for the peg, the problem is unsolvable.

 

[Steven G]

I think it should look like this..... please find the area...... TY

Why can't D be located below and to the left of C?
What have you tried to find the area?

 

[Ishuda]

I think it should look like this..... please find the area...... TY

The way you have the image drawn, i.e. 115m from the line containing the line segment AC instead of the more restrictive 115m from the leg AC, you have four possible places the peg could be. Of course two of them are more than 65m from the triangle and would give a grazing area of zero. One was mentioned by Jomo [to the left of and below C] and the other would be to the right of and below C. Given the one pictured leaves one more to the right of and above B. That last one looks like it will give the greatest grazing area covered but still short of a.) 3152.44 since the total area of the triangle is only 3600 m²

 

[Pradeep]

Area of the lawn too small for goat

I drew in AutoCad using your pic as reference. It seems that the area is small (13.1357 sq units). Are you sure this is the arrangement? Please check the attachments.