Answer:
The first set: 8, 15, and 17.
Step-by-step explanation:
<h3>Pair: 8, 15, 17</h3>
By the pythagorean theorem, a triangle is a right triangle if and only if
.
In this case,
.
.
In other words, indeed
. Hence, 8, 15, 17 does form a right triangle.
Similarly, check the other pairs. Keep in mind that the square of the longest side should be equal to the sum of the square of the two
<h3>Pair: 10, 15, 20</h3>
Factor out the common factor
to simplify the calculations.
![\text{longest side}^2 = 20^2 = 400](https://tex.z-dn.net/?f=%5Ctext%7Blongest%20side%7D%5E2%20%3D%2020%5E2%20%3D%20400)
.
.
Hence, by the pythagorean theorem, these three sides don't form a right triangle.
<h3>Pair: 12, 18, 22</h3>
.
.
.
Hence, by the pythagorean theorem, these three sides don't form a right triangle.
<h3>Pair: 7, 9, 11</h3>
.
<h3>
![\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 7^2 + 9^2\\ &=49+ 81 = 130 \end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%26%5Ctext%7Bfirst%20shortest%20side%7D%5E2%20%2B%20%5Ctext%7Bsecond%20shortest%20side%7D%5E2%20%5C%5C%20%26%3D%207%5E2%20%2B%209%5E2%5C%5C%20%26%3D49%2B%2081%20%3D%20130%20%5Cend%7Baligned%7D)
.</h3>
.
Hence, by the pythagorean theorem, these three sides don't form a right triangle.