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

`|WX|=|XY|=√(18) =3√(2)\:Units \:or\: 4.2 \:Units\\|WZ|=|YZ|=√(34) \:Units \:or\: 5.8 \:Units`

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|=√(18) =3√(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|=√(34) \:Units \:or\: 5.8 \:Units`