Which side lengths represent the sides of a right triangle?

a. 2,3,5
b. 7,24,25
c. 7,23,25
d. 12,16,21

For this case we have that every rectangle triangle complies with the Pythagorean theorem, that is, in every right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the respective lengths of the legs. So:

Option A:

It is not fulfilled

Option B:

Is fulfilled.

Option C:

It is not fulfilled

Option D:

Thus, it is observed that option b fulfills the Pythagorean theorem

Option B

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for