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?

Answer 1

Given

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.

To proof  

As given in the question and also shown in the diagram shown below

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

$\sqrt{256} =FA$

16cm = FA

Now in Δ DAG

DG² = AG² + DA²

13² = 12 ²+ DA²

169 -144 = DA²

25 = DA²

$\sqrt{25} =DA$

5cm = DA

Thus diagonal DF = DA + FA

= 5 + 16

= 21cm

Hence proved

Answer 2

The correct answer would be 21

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