sofia cuts a piece of felt in the shape of a kite for an art project. the top two sides measure 20 cm each…

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, $overline{eg}$, measures 24 cm. what is the length of the other diagonal, $overline{df}$? 5 cm 16 cm 21 cm 32 cm

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, $overline{eg}$, measures 24 cm. what is the length of the other diagonal, $overline{df}$? 5 cm 16 cm 21 cm 32 cm

Answer

Explanation:

Step1: Recall kite - diagonal property

The diagonals of a kite are perpendicular, and one diagonal bisects the other. Let the intersection of the diagonals (EG) and (DF) be point (O). Diagonal (EG = 24) cm, so (EO=OG = 12) cm.

Step2: Use the Pythagorean theorem in right - triangles

In right - triangle (EOD), (ED = 13) cm and (EO = 12) cm. By the Pythagorean theorem (a^{2}+b^{2}=c^{2}), where (c = ED), (a = EO), and (b = OD). So (OD=\sqrt{ED^{2}-EO^{2}}). Substitute (ED = 13) cm and (EO = 12) cm: (OD=\sqrt{13^{2}-12^{2}}=\sqrt{169 - 144}=\sqrt{25}=5) cm. In right - triangle (EOF), (EF = 20) cm and (EO = 12) cm. By the Pythagorean theorem, (OF=\sqrt{EF^{2}-EO^{2}}). Substitute (EF = 20) cm and (EO = 12) cm: (OF=\sqrt{20^{2}-12^{2}}=\sqrt{400 - 144}=\sqrt{256}=16) cm.

Step3: Calculate the length of diagonal (DF)

Since (DF=OD + OF), and (OD = 5) cm, (OF = 16) cm, then (DF=5 + 16=21) cm.

Answer:

21 cm