Nick has designed a diamond shaped kite as shown below. The measures of some sides of the kite are marked in the figure. Find the value of x.

Question

asked Aug 13, 2020 222k views

1 Answer

Piotr Stulinski · Answer 1 · 2020-08-19T18:25:08+0000

Answer:

Explanation:

In a kite, the diagonals are perpendicular. Hence
$\Delta DOC$ is a right angled triangle.

$DC=7\text{ }in,\text{ }OC=5\text{ }in$

From Pythagoras theorem, since
$\Delta DOC$ is a right angled triangle,
DO^(2)+OC^(2)=DC^(2) .

Area of
$\Delta DOC$ =
(1)/(2)* base* height

$=(1)/(2)* DO* OC=(1)/(2)* OP* DC\\(2√(6))*(5)=(7)*(OP)\\OP=3.499\text{ }in$

From diagram
OP=x

∴
$x=3.499\text{ }in$