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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.

Sagot :

iloveonedirection
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
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