Question

If in a rectangular, the angle between a diagonal and a side is 30${}^o$ and the length of the diagonal is $8$ cm, then the area of the rectangle is _____ .

• A. $16$$\sqrt{3}$ cm${}^2$
• B. $16$ cm${}^2$
• C. $\sqrt{3}$ cm${}^2$
• D. 16/$\sqrt{3}$ cm${}^2$

Answer 1

The correct option is A $16$$\sqrt{3}$ cm${}^2$

Referring figure, let ABCD be a rectangular in which $\angle$BAC = 30${}^o$ and AC = 8 cm

Then, cos30${}^o$ = $\frac{AB}{AC}\Rightarrow \frac{\sqrt{3}}{2}=\frac{AB}{8}\Rightarrow$ AB = 4$\sqrt{3}$ cm

and. sin 30${}^o$ = $\frac{BC}{AC}\Rightarrow \frac{1}{2}=\frac{BC}{8}\Rightarrow$ BC = 4 cm

$\therefore$ Area of rectangular = AB x BC
=4$\sqrt{3}$ x 4
= 16$\sqrt{3}$ cm${}^2$

So, option A is correct.