Question

you cut a picture into a right triangle for your scrapbook. the lenghts of the legs of the triangle are 4 inches and 6 inches. is the lenght of the hypotenuse a rational number?

Answer 1

Are you familiar with the Pythagorean theorem?

Answer 2

not so much..really not good at math

Answer 3

All the Pythagorean theorem says, is that if you have the lengths of the legs of a right triangle, then the length of the hypotenuse is the square root of the sum of square of the side lengths.

Numerically, if the leg lengths were \(a\) and \(b\), then the length of the hypotenuse would be \[\sqrt{a^2+b^2}\]

Answer 4

For example, if your side lengths were 3 and 4, then the hypotenuse would have length\[\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5\]

Answer 5

okay so i have 16 +36

Answer 6

That's the right first step. We have\[16+36=52\]Is 52 a perfect square?

Answer 7

when i square rooted it i got 7.2

Answer 8

so no then?

Answer 9

So \(\sqrt{52}\) is not an integer. That means that 52 is not a perfect square, and so \(\sqrt{52}\) can not possibly be rational.

Answer 10

thank you so much

Answer 11

You're welcome.