wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Rectangle of maximum area that can be inscribed in an equilateral triangle of side a will have area =

A
a232
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
a234
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
a238
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
none
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C a238
Let the side BC=a be chosen along x-axis and altitude AD be along y-axis.
AD2=AC2DC2=a2a24=3a24 AD=a32
Let QPSR be the rectangle inscribed in the triangle.
If A be its area, then A=2xy where (x,y) are the co-ordinates of vertex P which lies on line AC whose equation in intercept form is xa/2+y3a/2=1 or 2xa+2ya3=1(1)
Area A=2xy=x(12xa)a3 ...[ from (1) ]
dAdx=a3(14xa)=0
xa4 d2Adx2= ive and A is maximum.
A=a4(112)a3=a238
Ans: C

214586_184502_ans.bmp

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