Question

Which of the following represents side lengths that form a Pythagorean triple?

A. 7, 8, 9

B. 1, 2, 3

C. 4, 5, 6

D. 3, 4, 5

Answer 1

it is D 3,4,5

Answer 2

D. 3, 4, 5

Explanation:

Pythagorean theorem :
`Hypotenuse^2 = Perpendicular^2+Base^2`

If the given options satisfy the theorem .So, they form a Pythagorean triple.

Hypotenuse is the longest Side

A)7, 8, 9

Hypotenuse = 9

`Hypotenuse^2 = Perpendicular^2+Base^2`

`9^2 = 7^2+8^2`

`81 = 49+64`

`81 \\eq 113`

Hence not a Pythagorean triple.

B)1,2,3

Hypotenuse = 3

`Hypotenuse^2 = Perpendicular^2+Base^2`

`3^2 = 2^2+1^2`

`9 = 4+1`

`9 \\eq 5`

Hence not a Pythagorean triple.

C) 4,5,6

Hypotenuse = 6

`Hypotenuse^2 = Perpendicular^2+Base^2`

`6^2 = 3^2+4^2`

`36 = 9+16`

`36 \\eq 25`

Hence not a Pythagorean triple.

D)3,4,5

Hypotenuse = 5

`Hypotenuse^2 = Perpendicular^2+Base^2`

`5^2 = 3^2+4^2`

`25 = 9+16`

`25 = 25`

Hence a Pythagorean triple.

Hence Option D represents side lengths that form a Pythagorean triple