Question

Pythagorean theorem 19^2 + 21^2=x^2

Answer 1

`x=28.32\ units`

Explanation:

Given:

Expression for Pythagorean theorem:

`19^2+21^2=x^2`

By Pythagorean theorem (applied to right triangles only):

`c^2=a^2+b^2`

where
`c` represents hypotenuse or the longest side of triangle, while
`a` and
`b` represents the other two sides of the triangle.

Solving for hypotenuse i.e.
`x` in the given expression

`x^2=19^2+21^2`

⇒
`x^2=361+441`

⇒
`x^2=802`

Taking square root both sides:

⇒
`√(x^2)=√(802)`

∴
`x=28.32\ units` (Answer)

Answer 2

x = 28.32 units.

Explanation:

Given:

Longer leg = 21

Shorter leg = 19

Hypotenuse = x

To Find:

Hypotenuse = x = ?

Solution:

Pythagoras Theorem States that

`(\textrm{Hypotenuse})^(2) = (\textrm{Shorter leg})^(2)+(\textrm{Longer leg})^(2)`

Substituting of the given value above equation we get

`x^(2) =21^(2)+ 19^(2)\\ \\x^(2)=441 + 361\\\\x^(2)=802\\ \therefore x=\pm√(802) \\\textrm{as x cannot be negative}\\\therefore x=√(802)\\\\\therefore x=28.319\ units\\\therefore x=28.32\ units`