Question

The diagonal of a rectangle is 20 cm and it makes an angle of ${40}^{\circ }$ with one of its sides.The perimeter of the rectangle will be equal to $[sin{40}^{\circ }=1.64,cos{40}^{\circ }=0.76]$

• A. 65.25 cm
• B. 56.24 cm
• C. 48.5 cm
• D. 58.5 cm

Answer 1

The correct option is B

56.24 cm

Let the length and breadth of the rectangle be x and y respectively.

In right -angled triangle ABC

$sin{40}^{\circ }=\frac{CB}{AC}=\frac{y}{20}\Rightarrow y=20sin{40}^{\circ }=20\times 0.64=12.8cm$

$cos{40}^{\circ }=\frac{AB}{AC}=\frac{x}{20}\Rightarrow x=20cos{40}^{\circ }=20\times 0.76=15.32cm$

Perimeter of rectangle =$2(x+y)=2(15.32+12.8)$

$=56.24cm$