Answer:
The sides of a right triangle form an arithmetic sequence with the difference is described below in detail.
Step-by-step explanation:
Let's denominate the first term aa and the obvious difference dd. Therefore, your course enhances:
a, a+d, a+2da, a+d, a+2d
Now, these three terms form the sides of a right triangle. Since a+2da+2d is the highest (considering d > 0), we can state that it is the hypothenuse.
applying the Pythagorean Theorem:
a2+(a+d)2=(a+2d)2a2+(a+d)2=(a+2d)2
a2+a2+2ad+d2=a2+4ad+4d2a2+a2+2ad+d2=a2+4ad+4d2
3d2−a2+2ad=03d2−a2+2ad=0
(3d−a)(d+a)=0(3d−a)(d+a)=0
Therefore, your solutions are
3d=a3d=a
andd=−ad=−a
So if a = 3, d = 1. Therfore, one potential sequence is 3, 4, 5.
Similarly, if a = 6, then d = 2, so another potential sequence is 6, 8, and 10
