In a right triangle, there is arithmetic sequence. If the shortest side is 15 cm long, what is te length of the other 2 sides. ( hint use pytageron Therom)

To find the lengths of the other two sides in a right triangle with an arithmetic sequence, we can use the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, let's assume that the arithmetic sequence has a common difference of 'd'. Since the shortest side is 15 cm long, we can label it as 'a'. The other two sides can be labeled as 'a + d' and 'a + 2d'.

According to the Pythagorean theorem, we have the following equation:

a^2 + (a + d)^2 = (a + 2d)^2

Expanding and simplifying the equation, we get:

a^2 + a^2 + 2ad + d^2 = a^2 + 4ad + 4d^2

Rearranging the terms, we have:

a^2 + a^2 - a^2 + 2ad - 4ad + d^2 - 4d^2 = 0

Simplifying further:

a^2 - 2ad - 3d^2 = 0

Now, we can solve this quadratic equation using factoring or the quadratic formula to find the values of 'a' and 'd'. Once we find 'd', we can find the lengths of the other two sides by simply adding 'd' to 'a' and '2d' to 'a'.