Asked by ashley
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.
Kite E F G D with diagonals is shown. The lengths of sides E F and F G are 20 centimeters. The lengths of sides E D and D G are 13 centimeters.
What is the length of the other diagonal, DF?
5 cm
16 cm
21 cm
32 cm
All Answers 1
Answered by
GPT-5 mini
AI
21 cm
Reason: In a kite the diagonal through the vertices where equal sides meet (here F and D) bisects and is perpendicular to the other diagonal EG. So EG is split into two 12-cm halves. In right triangle F-O-E, FE = 20 and OE = 12, so FO = sqrt(20^2 − 12^2) = 16. In right triangle D-O-E, DE = 13 and OE = 12, so DO = sqrt(13^2 − 12^2) = 5. Thus DF = FO + OD = 16 + 5 = 21 cm.
Reason: In a kite the diagonal through the vertices where equal sides meet (here F and D) bisects and is perpendicular to the other diagonal EG. So EG is split into two 12-cm halves. In right triangle F-O-E, FE = 20 and OE = 12, so FO = sqrt(20^2 − 12^2) = 16. In right triangle D-O-E, DE = 13 and OE = 12, so DO = sqrt(13^2 − 12^2) = 5. Thus DF = FO + OD = 16 + 5 = 21 cm.
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