Question

Please help!!!

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.

Answer 1

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 \\eq 20^2`
Not a right triangle

(3) 15,26,30

`15^2 + 26^2 = 901`

`30^2 = 900`

`15^2 + 26^2 \\eq 30^2`
Not a right triangle

(4) 40,50,80

`40^2 + 50^2 = 4100`

`80^2 = 6400`

`40^2+50^2 \\eq 80^2`
Not a right triangle

#1 is a right triangle