The final verse of the description of the Courtyard of the Tabernacle in parshat Terumah provides the summary of the dimensions (length, width and height). Let's take a look:
18 The length of the court shall be an hundred cubits, and the breadth fifty every where, and the height five cubits of fine twined linen, and their sockets of brass.
18 אֹ֣רֶךְ הֶֽחָצֵר֩ מֵאָ֨ה בָֽאַמָּ֜ה וְרֹ֣חַב׀ חֲמִשִּׁ֣ים בַּחֲמִשִּׁ֗ים וְקֹמָ֛ה חָמֵ֥שׁ אַמּ֖וֹת שֵׁ֣שׁ מָשְׁזָ֑ר וְאַדְנֵיהֶ֖ם נְחֹֽשֶׁת׃
First and foremost, please note that the overall dimensions of the Courtyard are provided in the measurements of an overall dimensions of the Hangings. For example, the Length of the Courtyard is mentioned as being a one hundred(100) cubits of "fine twined linen" long - meaning that the dimensions of the Pillars along the length are not included. Same applies for the Width and Height of the Courtyard.
Of'course, one can say that this is exactly what the text implies(ie. the dimensions of the Pillars were not meant to be counted toward the overall dimensions of the Courtyard, and thus had to be located either inside or outside of the perimeter of the Court). However, if you would assume such positioning of the Pillars, it would create some serious problems.
First, I want to show the traditional interpretations and commentaries on the dimensions and layout of the Courtyard:
Here is an excerpt from a blog called Derech Etz Chaim Weekly Dvar by David Kohn, from his post on Parashat VaYakheil:
Rashi explains the Amud in the southeast corner counted as a southern pillar, not an eastern pillar. Likewise, the northeastern pillar must have counted towards the twenty Amudim on the north side. With another three Amudim for each, the “shoulders of the eastern wall could easily span fifteen amos, as the pasuk explicitly describes (27:14-15). Unfortunately, Rashi’s solution does not address the original difficulty with his description, for if the first southern pillar stood in the southeastern corner, and each subsequent pillar stood five amos apart, then the last pillar of neither the northern or southern walls reached the Mishkan’s western wall. With only ten Amudim left to span the fifty amos in the west, the Amudim would have to be spaced father than five amos apart to cover the necessary distance.
So, as you can see, Rashi explanation(even though somewhat correct) - does not work.
Mr. Kohn further writes:
So, as you can see the Masse Hoshef(Baraita) description is even more problematic than the description of Rashi. There is, however, one other traditional interpretation that almost solves the problem.The Ma’aseih Choshev suggests a completely different approach. By this alternative method, there were no Amudim in any of the corners of the Chatzer. To illustrate the design, here is a layout of the southern wall’s pillars: The first Amud of the south side stood two and a half amos from the southeast corner. The next Amud stood five amos away, and so on. The last Amud on the south side, therefore, stood two and a half amos from the southwest coner. Each of the sides followed a similar plan.
But the Ma’aseih Chosheiv does not explain what held the curtains up in the corners of the Chatzer. Presumably, a pole could extend across the tops of all the Amudim, and the curtains could hang off this pole. This in turn would explain how the southeast Kaseif hung off the first southern Amud in the southeast corner, provided that the pole count as part of the Amud. However, such an approach would not work so well with Rashi’s description of the vertical poles. Rashi asserts that the curtains were wrapped around the three tefach by six tefach poles that stuck out of the tops of the Amudim, not around any horizontal poles that spanned the length and width of the Chatzer. All in all, the Ma’aseih Chosheiv’s interpretation, like the Malbim’s, provides an elegant understanding of Rashi’s layout of the Amudim, but too requires an imagination to fill in the gaps within Rashi’s description.
Here is an excerpt from a blog called Al Pi Cheshbon by Eliezer Bulka. In his blog post "עמודי החצר" he writes:
Firstly, the Mizrachi suggests that the five amos referred to by Rashi are not five amos of space but rather five amos from the beginning of one beam to the beginning of the next.. This view is generally accepted amongst all those who deal with this problem with the obvious exception of the aforementioned Riva and Abarbanel. In pasuk 18, the Mizrachi infers from Rashi that the beams were one amah thick. Therefore, the actual space between each beam would be four amos and the thickness of the beam would complete the five amos. However, we have now only accounted for 95 amos. Therefore, the Mizrachi suggests that the north and south sides actually had 21 beams and the east and west had 11 but that the seemingly extra beam on each side belonged to the set of of beams of the side perpendicular to it. For instance, 21 beams were placed on the southern side of the courtyard. The beam in the southwest corner, though, was officially part of the western side. So, too, the beam in the northwest corner was not counted as part of the western beams but as part of the northern beams and so on. See illustration. With this arrangement another space of five amos is added to complete the 100 amos referred to in the pasuk.
But according to the Mizrachi's interpretation, the outer perimeter of the courtyard would be 102 amos by 52 amos.
The Levush HaOrah, another commentator on Rashi is unhappy with both the Mizrachi and the Gur Aryeh's explanations of Rashi in regards to the placement of the beams. From the fact that Rashi mentions the measurement of five amos between each beam more than just once, he infers that Rashi meant for this to be consistent throughout the entire perimeter of the courtyard. According to the Mizrachi the length of the north side, for instance, was really 102 amos and according to the Gur Aryeh it was 100. However, if you add up 21 beams each of one amah thickness and 20 spaces of four amos each, we are given 101 amos. So, too, on the east and west sides we would end up with 51 amos instead of 50 or 52. He concludes that the only way for the Mizrachi's figures to work out would be to say that one space on each of the four sides was actually one amah bigger. For the Gur Aryeh's figure to work one space would have to be one amah smaller. The Levush does not accept that such a lack of symmetry was present in the building of the Mishkan and offers a rather unique arrangement of the beams. Each of the beams were circular on the bottom for one amah and were inserted into circular holes in the copper sockets that held the beams in place. The beam itself was a semi-cylinder whose diameter was one amah. On each of the corners was placed a quarter-cylinder beam so that the curtain could wrap around it. See illustration. The thickness of this beam was only one half amah on either side. This removes one half amah one either end of each side of the courtyard. With this arrangement, the spaces between all of the beams were all four amos wide without any exception and the perimeter of the courtyard was exactly 100 amos by 50 amos as stated in the pesukim. Amongst all the interpretations mentioned thus far, this is by far the most symmetric and arithmetically accurate.
And even though the last interpretation is indeed comes very close to answering the question of the arrangement of the Courtyard, it still miserably fails to take in the account a simple fact: the dimensions and positioning of the Pillars does not really matter, because they are not located on the perimeter of the Courtyard(but rather on the inside of the perimeter).
And of'course, what makes this matter even worse, none of the traditional interpretations even attempt to reconcile the inconsistencies with the location of the Gate of the Courtyard and with the weight of the Pillars.
Therefore, the only way to solve the problem would be to understand, that the Actual Total Length of the Courtyard was 120 cubits and the Actual Total Width of the Courtyard was 60 cubits. Because only this approach would allow to put all of the details of the Courtyard together and thus - solve the problem.
This would allow satisfy the statement from the Baraita(HaMelech Hamishkan) about the location of the Gate(Masach) being ten(10) cubits further to the East. This would also resolve all difficulties with the positioning and distribution of the Pillars and the Hangings along the perimeter of the Courtyard. This would reconcile most of the statements in the traditional interpretations. And this would also put the total weight of all the parts of the Courtyard within the reasonable range. Here are the detailed diagrams:
[I.e.], the height of the partitions which was the width of the curtains.