Question

sofia cuts a piece of felt in the shape of a kite for an art project. the top two sides measure 20 cm each and the bottom two sides measure 13 cm each. one diagonal, eg, measures 24 cm. what is the length of the other diagonal, df? 5 cm 16 cm 21 cm 32 cm

Explanation:

Step1: Use the property of kite's diagonals

The diagonals of a kite are perpendicular, and one diagonal is bisected by the other. Let \(EG = 24\) cm, so \(EO=\frac{EG}{2}=12\) cm (\(O\) is the intersection point of the diagonals).

Step2: Apply Pythagorean theorem in right - angled triangles

In right - triangle \(FEO\), \(FE = 20\) cm, \(EO = 12\) cm. By Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = FE\), \(a = EO\), and \(b = FO\). Then \(FO=\sqrt{FE^{2}-EO^{2}}=\sqrt{20^{2}-12^{2}}=\sqrt{400 - 144}=\sqrt{256}=16\) cm.
In right - triangle \(DEO\), \(DE = 13\) cm, \(EO = 12\) cm. By Pythagorean theorem, \(DO=\sqrt{DE^{2}-EO^{2}}=\sqrt{13^{2}-12^{2}}=\sqrt{169 - 144}=\sqrt{25}=5\) cm.

Step3: Calculate the length of \(DF\)

Since \(DF=FO + DO\), \(DF=16 + 16=32\) cm.

Answer:

\(32\) cm