Given the length of three sides of a triangle, which is a right triangle?

(1) 10,26,24

(2) 20,12,18

(3) 30,15,26

(4) 40,50,80

And also explain why it is the answer.

Pythagorean Theorem: \( a^2 + b^2 = c^2 \)

c represents the longest side of the triangle

If the triangle is a right triangle, the Pythagorean theorem will be true.

(1) 10,24,26

\( 10^2 + 24^2 = 676 \)

\( 26^2 = 676 \)

\( 10^2 + 24^2 = 26^2 \)

Right Triangle

(2) 12,18,20

\( 12^2 + 18^2 = 468 \)

\( 20^2 = 400 \)

\( 12^2 + 18^2 \neq 20^2 \)

Not a right triangle

(3) 15,26,30

\( 15^2 + 26^2 = 901 \)

\( 30^2 = 900 \)

\( 15^2 + 26^2 \neq 30^2 \)

Not a right triangle

(4) 40,50,80

\( 40^2 + 50^2 = 4100 \)

\( 80^2 = 6400 \)

\( 40^2+50^2 \neq 80^2 \)

Not a right triangle

#1 is a right triangle

there has to be an answer because those are the only choices. your write that the Pythagorean theorem will be true if it is a right triangle but none of them work. I was thinking if it is 4 because in a right triangle, the c^2 side has the greatest length of all the other sides.

so would 4 be the answer

1 is the answer. i plugged in all the values. the order your numbers are in are not necessarily (a, b, c). c=the highest number, so for instance in number 1, 26 would be "c" not 24