1) We know that, an odd number's square will be odd. Adding two odd numbers square will give you even number. So adding squares of two odd numbers will give you an even number.
2) Take 19 and other prime number.
3) Add their squares. Divide it by 2.
4) Find in how many ways the last digit can be formed.
5) Try to express the number obtained in step 3 as square of two numbers. You may write natural numbers and their squares separately.
6) Remember 2,3,7 and 8 do not come at the end of (unit place of) a perfect square.
7) Discard those possibilities.
8) 1,3,5,7 and 9 can come at / as last digit in following ways.
1: 0 & 1 or 5 & 6
3: 4 & 9
5: 1 & 4; 5 & 0 or 6 & 9
7: 1 & 6
9: 4 & 5 or 0 & 9.
For above mentioned step 5) consider natural numbers up to square root of the largest perfect square less than or equal the sum obtained step 3.
9) We know that sum of two sides of a triangle is greater than third side.
Check whether all the three triangles so formed satisfy this condition.
10) You can create another sum. If three sides of larger triangle are obtained as a-b-2d and median on side 2d as c; the other sum (triangle) is a-b-2c and its median will be d.
- Thursday, the midnight of 22 Nov 18 2:12 a.m. 23 Nov 2018.
3 Prostrations to Shree Saibaba, Shirdi, Dist. Ahmednagar, Maharashtra, India!!!
For example:
In triangle ABC, sides are as given below. Find length of median AM on side BC.
1) AB=13, AC=29, BC=24.
2) AB=13, AC=29, BC=38.
