Question

Maci and I are making a small kite. Two sides are 10". Two sides are 5". The shorter diagonal is 6". Round all your answers to the nearest tenth. What is the distance from the peak of the kite to the intersection of the diagonals? What is the distance from intersection of the diagonals to the top of the tail? What is the length of the longer diagonal?

Answer 1

The distance from the peak of the kite to the intersection of the diagonals is
`√(91)` inches.

The distance from the intersection of the diagonals to the top of the tail is 4 inches.

Length of the longer diagonal =
`√(91) +4` inches.

Explanation:

Please refer to the attached figure.

It is given that the length of the shorter diagonal = 6 inches.

BD = 6

BE =
`(1)/(2) BD`

= 3 inches

In right triangle AEB,

`AE^(2) =AB^(2) -BE^(2)`

`=10^(2) -3^(2)`

= 100 - 9

= 91

`AE=√(91)`

Hence, the distance from the peak of the kite to the intersection of the diagonals is
`√(91)` inches.

From the right triangle BEC,

`EC^(2) =BC^(2) -BE^(2)`

=
`5^(2) -3^(2)`

= 25 - 9

= 16

EC = 4 inches

Hence, the distance from the intersection of the diagonals to the top of the tail is 4 inches.

Length of the longer diagonal = AC = AE + EC =
`√(91) +4` inches.