Answer:
D. 3, 4, 5
Step-by-step explanation:
Pythagorean theorem : [tex]Hypotenuse^2 = Perpendicular^2+Base^2[/tex]
If the given options satisfy the theorem .So, they form a Pythagorean triple.
Hypotenuse is the longest Side
A)7, 8, 9
Hypotenuse = 9
[tex]Hypotenuse^2 = Perpendicular^2+Base^2[/tex]
[tex]9^2 = 7^2+8^2[/tex]
[tex]81 = 49+64[/tex]
[tex]81 \neq 113[/tex]
Hence not a Pythagorean triple.
B)1,2,3
Hypotenuse = 3
[tex]Hypotenuse^2 = Perpendicular^2+Base^2[/tex]
[tex]3^2 = 2^2+1^2[/tex]
[tex]9 = 4+1[/tex]
[tex]9 \neq 5[/tex]
Hence not a Pythagorean triple.
C) 4,5,6
Hypotenuse = 6
[tex]Hypotenuse^2 = Perpendicular^2+Base^2[/tex]
[tex]6^2 = 3^2+4^2[/tex]
[tex]36 = 9+16[/tex]
[tex]36 \neq 25[/tex]
Hence not a Pythagorean triple.
D)3,4,5
Hypotenuse = 5
[tex]Hypotenuse^2 = Perpendicular^2+Base^2[/tex]
[tex]5^2 = 3^2+4^2[/tex]
[tex]25 = 9+16[/tex]
[tex]25 = 25[/tex]
Hence a Pythagorean triple.
Hence Option D represents side lengths that form a Pythagorean triple
