Question

find the lenghth of hypotonuse if one lengh is 6 , leave it simplified redical form

Answer 1

We are given a right triangle and we are asked to determine the length of the hypotenuse. To do that we will use the Pythagorean theorem:

$h^2=a^2+b^2$

Where "h" is the hypothenuse and a and b the other two sides. In this case, the two sides are equal since the triangle is 45 - 45 - 90. We have the following values:

$\begin{gathered} a=6 \\ b=6 \end{gathered}$

Substituting:

$h^2=(6)^2+(6)^2$

Solving the operations:

$\begin{gathered} h^2=36+36 \\ h^2=2(36) \end{gathered}$

Taking square root to both sides:

$h=\sqrt[]{2(36)}$

Now we will use the following property:

$\sqrt[]{ab}=\sqrt[]{a}\times\sqrt[]{b}$

Applying the property:

$h=\sqrt[]{2}\times\sqrt[]{36}$

Solving the operations:

$h=6\sqrt[]{2}$

And thus we have found the hypothenuse in its most simplified form.