Question

find the unknown side length. simplify answers that are radicals . tell whether the side lengths form a Pythagorean triple

Answer 1

We use the Pythagorean Theorem to answer this:
a²+b²=c²
In our case,

`(√(7))^2+b^2=(√(19))^2`

`7+b^2=19`
Subtract 7 from each side:

`7+b^2-7=19-7 \\b^2=12`
Take the square root of both sides:

`√(b^2)=√(12)=√(4*3)=2√(3)`
Although these numbers work in the Pythagorean theorem, they are not Pythagorean triples, as they are not integers.