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by leonswati » Mon Apr 23, 2012 8:42 am
The shape of an ancient druid castle is rectangular solid. Each of its dimensions is an integral number of meters. The castle is surrounded by a moat of 5 meters wide. The height of the castle is twice its length and three times its width. What is the height in meters if the area of the castle floor and the surface of the surrounding moat are equal?

I took the length = L, width=2L/3 and height = 2L .... But after this I got stuck. Any help would be appreciated... Thanks...
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by Shalabh's Quants » Mon Apr 23, 2012 10:19 am
leonswati wrote:The shape of an ancient druid castle is rectangular solid. Each of its dimensions is an integral number of meters. The castle is surrounded by a moat of 5 meters wide. The height of the castle is twice its length and three times its width. What is the height in meters if the area of the castle floor and the surface of the surrounding moat are equal?

I took the length = L, width=2L/3 and height = 2L .... But after this I got stuck. Any help would be appreciated... Thanks...
Image

Pl. see the image above.

Surface area of Moat = (10+w).(L+10) - w.L;

Area of castle = w.L

As Surface area of Moat = Area of castle;

hence, (10+w).(L+10) - w.L = w.L;

Replace w = 2L/3, we get L = 30 mtr.
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by pemdas » Mon Apr 23, 2012 10:32 am
first the moat's dimension will be the same as ones of the castle L and W. Hence the total surface area of moat will be 2*(5L+5W)+4*(5^2) or moat's surface=10L+10W+100. Since moat's surface is the same as castle's floor area, we obtain W*L=10L+10W+100. We are given H=3W=2L and can represent W through L anyways --> W*L=10L+10W+100 along with W=2L/3 can be expressed as (2/3)L^2=10L+20L/3+100 and solving for L will give us L^2-25L-150=0, L=30 or -5. We discard the negative value and keep only L=30 to obtain H=3L or H=60.
answer 60

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leonswati wrote:The shape of an ancient druid castle is rectangular solid. Each of its dimensions is an integral number of meters. The castle is surrounded by a moat of 5 meters wide. The height of the castle is twice its length and three times its width. What is the height in meters if the area of the castle floor and the surface of the surrounding moat are equal?

I took the length = L, width=2L/3 and height = 2L .... But after this I got stuck. Any help would be appreciated... Thanks...
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