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: 21

Sofia cuts a piece in the shape of a kite for an art project

top two sides measure 20 cm each

bottom two sides measure 13 cm each.

One diagonal, EG, measures 24 cm

Find out the length of the other diagonal, DF.

explanation-

DE = EF = 20cm

DG = GF = 13cm

EG = 24cm

DF = ?

In kite shape

One diagonal is the perpendicular bisector of the other diagonal.

i. e EG is the perpendicular bisector of DF

i. e EG is divided into two equal parts

thus EA = AG = 12cm

in Δ EAF

By applying the pythagorus theorem

we have

EF² = FA² + EA²

20² = 12² + FA²

400 - 144 = FA²

256 = FA²

16cm = FA

Now in Δ DAG

DG² = AG² + DA²

13² = 12 ² + DA²

169 - 144 = DA²

25 = DA²

5cm = DA