Question

c
In the figure, ABCD is a rectangle with ZBDA = 60° &
BD = 10 cm .
Find the sides of the rectangle and also the area of the
rectangle.
(write the answer correct up to 3 places of decimal)​

Answer 1

Answer:

The length of diagonals 40 cm and length of BC is 203=34.6cm

Step-by-step explanation:

Given a rectangle ABCD in which AB=20 cm and ∠BAC=60°

we have to find the length of side BC and diagonals AC and BD.

In ΔABC, by trigonometric ratios

\cos\angle A=\frac{base}{hypotenuse}=\frac{AB}{AC}cos∠A=hypotenusebase=ACAB

\cos 60=\frac{20}{AC}cos60=AC20

\frac{1}{2}=\frac{20}{AC}21=AC20

AC=20\times 2=40 cmAC=20×2=40cm

As diagonals of rectangles are equal

⇒ AC=BD=40 cm

\tan\angle A=\frac{Perpendicular}{Base}=\frac{BC}{AB}tan∠A=BasePerpendicular=ABBC

\tan60^{\circ}=\frac{BC}{20}tan60∘=20BC

\sqrt3=\frac{BC}{20}3=20BC

BC=20\sqrt3=34.6 cmBC=203=34.6cm