Lets draw the square first.
As you can see in the diagram, the distance between one corner and the opposite side is the diagonal of the rectangle which divides it into tow right triangles. Since we know that in a square all the lengths have the same measure, the legs of our triangle are going to measure 250 ft.
Now, the only thing left to do is apply the Pythagorean theorem to find the hypotenuse of our triangle which is no other than the diagonal of our square:



We can conclude that the distance <span>from one corner of the courtyard to the opposite corner is 353.6 ft.</span>
The distribution of the possible digits of the numbers are
1.) 9, 9, 9, 9, 3 [Number of arrangements = 5! / 4! = 120 / 24 = 5]
2.) 9, 9, 9, 8, 4 [Number of arrangements = 5! / 3! = 120 / 6 = 20]
3.) 9, 9, 9, 7, 5 [Number of arrangements = 5! / 3! = 120 / 6 = 20]
4.) 9, 9, 9, 6, 6 [Number of arrangements = 5! / (3! x 2!) = 120 / 12 = 10]
5.) 9, 9, 8, 8, 5 [Number of arrangements = 5! / (2! x 2!) = 120 / 4 = 30]
6.) 9, 9, 8, 7, 6 [Number of arrangements = 5! / 2! = 120 / 2 = 60]
7.) 9, 9, 7, 7, 7 [Number of arrangements = 5! / (3! x 2!) = 120 / 12 = 10]
8.) 9, 8, 8. 8, 6 [Number of arrangements = 5! / 3! = 120 / 6 = 20]
9.) 9, 8, 8, 7, 7 [Number of arrangements = 5! / (2! x 2!) = 120 / 4 = 30]
10.) 8, 8, 8, 8, 7 [Number of arrangements = 5! / 4! = 120 / 24 = 5]
Number of 5 digit numbers whose digit sum up to 39 = 5 + 20 + 20 + 10 + 30 + 60 + 10 + 20 + 30 + 5 = 210
Answer:
Since a Pythagorean triple is three positive integers a, b, and c such that (a^2)+(b^2)=(c^2), where a and b are the two legs, and c is the hypotenuse, first take the sum of the squares of the two legs and make an estimate. For example, 3, 4, and 5 is a Pythagorean triple since 9+16=25.