Question

The area of a kite is 6 times the length of its shortest
diagonal minus 9 and its longest diagonal is 6 cm long.

1) Find the length of the shortest diagonal,

2) Find the area of the kite,

3) If the shortest diagonal is given as 3cm, find the length
of the longest diagonal.

Answer 1

Answer:

Area of kite =6a-9(where a=length of its shortest diagonal)cm

where the longest diagonal =6cm

1::

Area of kite =(longest diagonal ×shortest diagonal )/2

6a-9 = (6×a)/2

2(6a-9) = 6a

12a-18 = 6a

12a-6a = 18

6a = 18

a = 18/6

a = 3

shortest diagonal length =3cm

2:

area of kite=6a-9

a = 3

Area= (6×3) -9

= 18-9

= 9

area of kite=9cm

(or)

area of kite =longest diagonal ×shortest diagonal/2

= 6×3/2

=18/2

=9

area of kite = 9cm

3::

if the shortest diagonal =3cm

then,

area of kite = 9cm

9 =(a×3)/2(a=longest diagonal)

9×2=3a

18=3a

18/3= a

a=6cm

longest diagonal length =3cm