Question

Which of the following sets of numbers is a Pythagorean triple?

77, 35, 112
70, 35, 78
75, 36, 83
77, 36, 85

Answer 1

Hey!


Now, to find the Pythagorean triple we must first start off by finding the quare of the two smallest numbers in the data set. After we find the square of both of them, we will then add them together. If our product does not equal the square of our remaining number in the data set, then it is not a Pythagorean triple. If it does, then it is a Pythagorean triple.

So, let's start with the first set of numbers. Since the smallest numbers in the first number set are 77 and 35, we'll start by find the square of those.

Square of
`77^(2)` - 5,929

Square of
`35^(2)` - 1,225

And now we add those together.

5,929 + 1,225 = 7154

And now to determine that this it is a Pythagorean triple we'll find the square of the remaining number in our data set and if it DOES equal the same as our product then it is a Pythagorean triple.


`112^(2)` - 12,544

7154
`\\eq` 12544

So, since these do not equal this is not a Pythagorean triple.

We'll do the same for the next three sets.

SET #2


`70^(2)` - 4900


`35^(2)` - 1225

4900 + 1225 = 6125


`78^(2)` - 6084

6125
`\\eq` 6084

Not equal so this is not a Pythagorean triple.

SET #3


`75^(2)` - 5625


`36^(2)` - 1296

5625 + 1296 = 6921


`83^(2)` - 6889

6921
`\\eq` 6889

Not equal so this is not a Pythagorean triple.

SET #4


`77^2` - 5929


`36^(2)` - 1296

5929 + 1296 = 7225


`85^(2)` - 7225

7225 = 7225

These numbers are equal.

So, this mean that the last set is a Pythagorean triple.

Hope this helps!


- Lindsey Frazier ♥

Answer 2

Hey there!

You have to use the Pythagorean Theorem

a² + b² = c²

1st choice -

a = 35
35² = 35 · 35 = 1,225

b = 77
77² = 77 · 77 = 5,929

1,225 + 5,929 = 7,154

√7154 = 84.6 x

2nd choice -

a = 35
35² = 35 · 35 = 1,225

b = 70
70² = 70 · 70 = 4,900

1,225 + 4,900 = 6,125

√6,125 = 78.3 x

3rd choice -

a = 36
36² = 36 · 36 = 1,296

b = 75
75² = 75 · 75 = 5,625

1,296 + 5,625 = 6,921

√6,921 = 83.2 x

4th choice -

a = 36
36² = 36 · 36 = 1,296

b = 77
77² = 77 · 77 = 5,929

1,296 + 5,929 = 7,225

√7,225 = 85 ✔

Answer ⇒ Last set ⇒ D

A. 77, 35, 112
B. 70, 35, 78
C. 75, 36, 83
D. 77, 36, 85 ✔

Hope this helps! :)