# How do I find the value of x?Do the side lengths form a pythagorean triple?

Mar 16, 2017

$20$

#### Explanation:

Yes, the sides form a triple (it is a $3 , 4 , 5$ triangle, except on a bigger scale ($4$ times bigger)).

By the Pythagorean Theorem,

${a}^{2} + {b}^{2} = {c}^{2}$.

In this case,
${12}^{2} + {16}^{2} = {c}^{2}$
$400 = {c}^{2}$, and since $c$ is a side length, it must be the positive answer to the square root, or $20$.

Mar 16, 2017

$x = 20$; See link

#### Explanation:

Use the Pythagorean theorem (${a}^{2} + {b}^{2} = {c}^{2}$)

Lets label the right triangle such that:
$a = 12$
$b = 16$
$c = x$

Thus,

${12}^{2} + {16}^{2} = {x}^{2}$

$144 + 256 = {x}^{2}$

$400 = {x}^{2}$

$\sqrt{400} = x$

$20 = x$

So our missing side, $c$ is $20$

We can now say that the sides of our triangle are $12 , 16 , 20$

I've included a link that lists a couple of Pythagorean triples (a couple because they are infinitely many).

https://www.mathsisfun.com/numbers/pythagorean-triples.html

Mar 16, 2017

$x = 20$, Yes.

#### Explanation:

$12 = 4 \times 3$

$16 = 4 \times 4$,

$3$, $4$, $5$ is a Pythagorean triple, so

$x = 4 \times 5$