Answer :
Pythagorean Theorem: [tex]a^2 + b^2 = c^2[/tex]
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
[tex]10^2 + 24^2 = 676[/tex]
[tex]26^2 = 676[/tex]
[tex]10^2 + 24^2 = 26^2[/tex]
Right Triangle
(2) 12,18,20
[tex]12^2 + 18^2 = 468[/tex]
[tex]20^2 = 400[/tex]
[tex]12^2 + 18^2 \neq 20^2[/tex]
Not a right triangle
(3) 15,26,30
[tex]15^2 + 26^2 = 901[/tex]
[tex]30^2 = 900[/tex]
[tex]15^2 + 26^2 \neq 30^2[/tex]
Not a right triangle
(4) 40,50,80
[tex]40^2 + 50^2 = 4100[/tex]
[tex]80^2 = 6400[/tex]
[tex]40^2+50^2 \neq 80^2[/tex]
Not a right triangle
#1 is a right triangle
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
[tex]10^2 + 24^2 = 676[/tex]
[tex]26^2 = 676[/tex]
[tex]10^2 + 24^2 = 26^2[/tex]
Right Triangle
(2) 12,18,20
[tex]12^2 + 18^2 = 468[/tex]
[tex]20^2 = 400[/tex]
[tex]12^2 + 18^2 \neq 20^2[/tex]
Not a right triangle
(3) 15,26,30
[tex]15^2 + 26^2 = 901[/tex]
[tex]30^2 = 900[/tex]
[tex]15^2 + 26^2 \neq 30^2[/tex]
Not a right triangle
(4) 40,50,80
[tex]40^2 + 50^2 = 4100[/tex]
[tex]80^2 = 6400[/tex]
[tex]40^2+50^2 \neq 80^2[/tex]
Not a right triangle
#1 is a right triangle
