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. 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

Answer 1

Answer:

21 cm

Step-by-step explanation:

Let say Diagonal intersect at O

Diagonal of kite are peprpendicular to each other

=> Δ   EFO  ≅ Δ GFO

as EF = FG = 20 cm   & FO is common

hence EO = GO  = EG/2= 24/2 = 12 cm

in Δ EFO

FO² = EF² - EO² = 20² - 12² = 400 - 144

=> FO² =  256

=> FO = 16

in Δ EOD

DO² = ED² - EO² = 13² - 12² = 169 - 144

=> DO² = 25

=> DO = 5

DF = DO + FO = 5 + 16 = 21 cm

length of the other diagonal, DF = 21 cm