Which of the following represents side lengths that form a Pythagorean triple?A. 7, 8, 9B. 1, 2, 3C. 4, 5, 6D. 3, 4, 5
Accepted Solution
A:
Answer:D. 3, 4, 5Step-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 SideA)7, 8, 9Hypotenuse = 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)1,2,3Hypotenuse = 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) 4,5,6Hypotenuse = 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)3,4,5Hypotenuse = 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