The Importance of the Dimensions of Noah's Ark

In Parshat Noach, when Noach receives the commandment to build an ark, he is given exact dimensions for the measurements of the ark. Why and what is the significance of the stated sizes?

This is how you shall construct it: The ark's length shall be 300 cubits, its width 50 cubits, and its height 30 cubits. 

Bresheit 6:15

The commentary Kli Yakar remarks on this situation giving two explanations.

1. The size of the ark is specified in order to show the miracle that took place with the building of the ark since the animals that went into the ark, like elephants, were much largely than the stated dimensions would accommodate.
2. The second reason relates to the amounts for the stated dimensions: 300 cubits and 30 cubits. These are multiples of 15. What is the significance of 15?

When looking at the words for Man and Woman, they are איש and אשה where the two letters that are not common between the two words are י and ה whose combined numerical value is 15. These two letters are also two of the four letters that comprise G-d's sacred name. The people of the generation of the flood exhibited a degenerate level of behavior, where literally nothing was sacred. There was no sanctity to marriage, and women were freely taken upon whim.

When you remove these uncommon letters from these two words, you are left with the word אש which is Fire. So when the generation of the flood removed sacredness, and essentially G-d, from their midst, they really lit the fire that set in motion The Flood.

The Kli Yakar continues by showing the significance of the number 15. First from Parshat Noach, 15 comes up in several places:

• the dimensions of the ark: 300 (15x20), 30(15x2)
• the days at sear for the ark: 150 (15x10) Bresheit 7:24
• the waters had surged upward 15 cubits (Bresheit 7:20)

The Kli Yakar brings in other relevant areas. King Hezekiah was afflicted with a deadly illness (leprosy) as punishment for remaining unmarried; Babylonian Talmud, Tractate Semachot, (47a). Later when he repented and became more religious, he was rewarded with 15 years added to his lifetime.
King David wrote 15 'Shirei haMaalot' - psalms of ascent, specifically in recognition of the disregard of G-d by the generation of the flood.

The Talmud teaches that there was a semicircular flight of 15 stairs in the temple at Jerusalem leading from the women's district up to men's vestibule.

The presence throughout this Parshah of 15, essentially the presence of G-d, and its unique importance in Jewish history and tradition, shows that the choice of exact size for the dimensions of the ark relate an important concept. The Torah constantly works on the principle of Measure for Measure (Midah Kneged Midah), just as the generation of the flood distanced themselves from the inherent nature of G-d, this same essence of G-d was woven into Noach and his experience.

We learn that in the ideal family life, there are three parties to creation - the mother, the father and G-d. It is G-d that plays a central, and so symbolized by the presence of his name in the words for man and woman. When G-d is removed from this scenario, all that remains is Fire.

It is important to realize the opposite.  The generation of the flood ran rampant, devoid of basic morality, tossing any sacredness and sanctity aside, and removing the essence of G-d from their realm, bringing about the greatest destruction upon the world, leaving devastation everywhere.
So also, when we do the opposite, and bring G-d into our lives, and make G-d and inherent part of our family relations, thus we enable great source of creation in the world. The ever-growing presence of G-d in our lives serves to not only nurture our faith but also to enhance the world to the opposite lengths that the flood brought destruction.