CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
0
You visited us 0 times! Enjoying our articles? Unlock Full Access!
Question


ABCD is a rectangle such that CAB=60 and AC=a units.
The area of rectangle ABCD is ______.

A
32a2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
23a2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
34a2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
38a2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C 34a2
ABCD is a rectangle. HenceABC=900.



So, in ΔABC, right-angled at B,
Sin θ=oppositehypotenuseSin 600=BCAC
On substituiting the value of Sin 600=32 and AC = a units, we get

32=BCaBC=32a---------(i)

Cos θ=adjacenthypotenuseCos 60=ABAC
On substituiting the value of Cos 600=12 and AC = a units, we get
12=ABaAB=a2---------(ii)

From(i) and (ii),
So, area of the rectangle = length × breadth
=AB×BC=a2×32a=3a24

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Height and Distances
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon