Question

Theorem 8.18 and the Pythagorean Theorem to find the side lengths of the kite . Write the lengths in simplest radical form and as a decimal rounded to the tenth place .

Answer 1

Answer:

$|WX|=|XY|=\sqrt{18} =3\sqrt{2}\:Units \:or\: 4.2 \:Units\\|WZ|=|YZ|=\sqrt{34} \:Units \:or\: 5.8 \:Units$

Step-by-step explanation:

Theorem: The diagonals of a kite are perpendicular.

Let O be the point of intersection of the diagonals,

Applying Pythagoras Theorem, in right triangle WOX

$|WX|^2=|WO|^2+|OX|^2\\|WX|^2=3^2+3^2=18\\|WX|=\sqrt{18} =3\sqrt{2}\:Units \:or\: 4.2 \:Units$

Applying Pythagoras Theorem, in right triangle WOZ

$|WZ|^2=|WO|^2+|OZ|^2\\|WX|^2=3^2+5^2=34\\|WZ|=\sqrt{34} \:Units \:or\: 5.8 \:Units$