Which of the following will form a right triangle?
7, 24, 25
7, 23, 24
7, 25, 26

I noticed a pattern:

Any side with an odd value followed by 2 consecutive numbers such as their sum is the square of the side will form a right triangle.

For instance:

3, 4, 5

3^2 = 4+5

Another one:

5, 12, 13

5^2 = 12+13

Check with Pythagorean Theorem:

a^2 + b^2 = c^2

3^2 + 4^2 = 5^2

9 + 16 = 25

5^2 + 12^2 = 13^2

25 + 144 = 169

Now we can apply that to these 3 options:

7, 25, 26

Check with Pattern: 7^2 25+26

Check with Pythagorean Theorem: 7^2 + 25^2 26^2

7, 23, 24

Check with Pattern: 7^2 23+24

Check with Pythagorean Theorem: 7^2 + 23^2 24^2

7, 24, 25

Check with Pattern: 7^2 = 24+25

Check with Pythagorean Theorem: 7^2 + 24^2 = 25^2

So that's our 7, 24, 25

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl

the answer is a if my teacher taught me correct