Question

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.

Answer 1

Answer:

x = 3.499 in

Step-by-step 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 $\Delta DOC$ = $\frac{1}{2}\times base\times height$

$=\frac{1}{2}\times DO\times OC=\frac{1}{2}\times OP\times DC\\(2\sqrt{6})\times(5)=(7)\times(OP)\\OP=3.499\text{ }in$

From diagram $OP=x$

∴ $x=3.499\text{ }in$