Question

the figure below is a kite. solve for w, x, and y

Explanation:

Step1: Find \( w \)

In a kite, the diagonals are perpendicular bisectors of each other. So, \( w = 1.6\) cm (by the property of kite's diagonal bisecting each other).

Step2: Find \( x \)

Since the diagonals of a kite are perpendicular, we can use the angle - property. In the right - triangle formed by the diagonals, \( x = 48^{\circ}\) (by the property of kite's angles bisected by the diagonal).

Step3: Find \( y \)

Using the Pythagorean theorem in the right - triangle with sides \( 1.6\) cm and \( y \) (hypotenuse \( 3.4\) cm). Let's recall the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 3.4\) and \(a = 1.6\). Then \(y=\sqrt{3.4^{2}-1.6^{2}}=\sqrt{(3.4 + 1.6)(3.4 - 1.6)}=\sqrt{5\times1.8}=\sqrt{9}=3.0\) cm.

Answer:

\( w = 1.6\) cm, \( x = 48^{\circ}\), \( y = 3.0\) cm