Question

In the figure <CAB=30°, <CPB=60°. AP 10 centimeters. Area of the rectangle ABCD is.............................. square centimeters.

• A. 25(2+√3)
• B. 25 (1+√3)
• C. 75
• D. 75√3

Answer 1

Answer:

D. 75√3

In △ APC

∠ APC = 180° - 60° = 120°

So ∠ACP = 180° - (120 + 30 ) = 30°

Triangle APC is an isosceles triangle

So AP = PC = 10 cm

In △ PBC

∠ PBC = 90°

∠ BPC = 60°

∠ PCB = 30°

Ratio 30° : 60° : 90° = 1 : √3 : 2

PC = 2 = 10cm

PB = 1 = 5

BC = 5√3

So,

AB = 15 cm

BC = 5√3

Area of ABCD = length × breadth

= 15 × 5√3

= 75√3 cm²