Question

What is ABCD?

Answer 1

`color(blue)("Perimeter of the kite " = 125.42'`

Explanation:

ABCD is a KITE.

It's properties are

1. Diagonals intersect each other at right angles.

2. One diagonal (AC) is bisected by (BC) at O.

3. AB = BC, AD = CD.

`hat ADC = 40^@, hatABC = 80^@, AC = 28 ft`

`"Also given : " AB = BC, AD = CD`

In `Delta ABC, AB = BC, AO = CO, BO " common"`

Hence `Deltas " " AOB, COB " congruent"`

`hat (ABO) = hat (CBO) = hat (ABC) / 2 = 80 / 2 = 40^@`

Hence `hat BAO = hat BCO = 180 - 90 - 40 = 50^@`

Also `AO = CO = AC / 2 = 28 / 2 = 14`

`:. (AB) / sin 90 = (AO) / sin 40 = (BO) / sin 50` Applying sin law.

`AB = BC = (AO) / sin 40 = 14 / sin 40 = 21.78'`

Similarly, `Deltas ADO, CDO " congruent"`

`hat (ADO) = hat (CDO) = hat (ADC) / 2 = 40 / 2 = 20^@`

`:. AD = CD = (AO) / sin 20 = 14 / sin 20 = 40.93'`

`"Perimeter of the kite ABCD " = AB + BC + CD + DA`

`=> 21.78 + 21.78 + 40.93 + 40.93 = 125.42'`