Click to Chat

1800-1023-196

+91-120-4616500

CART 0

• 0

MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
`        A large window has the shape of a rectangle surmounted by an equilateral triangle.If the perimeter of the window is 12 metres find the dimensions of the rectangle that will produce the largest area of the window.`
6 years ago

```							let the width and length of rectangle are y and x respectively .each sides of the triangle will be x.so Total area of window S = area of rectangle +area of trianle=xy+(sqrt3)/4 .x2and total perimeter 3x+2y=12 =>y=(12-3x)/2S= x(12-3x)/2 +sqrt3/4.x2=6x+(sqrt3/4 -3/2) x2ds/dx=6+2(sqrt3/4 -3/2 ) xput ds/dx=0then we get x=12/(6-sqrt3)=4(6+sqrt3)/11d2s/dx2=2(sqrt3/4 -3/2) <0so S ios maxima at x=4(6+sqrt3)/11hence x=4(6+sqrt3)/11 and y=12- 12(6+sqrt3)/11=12(5-sqrt3)/11Hence the dimensions of the rectangle are 4(6+sqrt3)/11, 12(5-sqrt3)/11Thanks & RegardsRinkoo GuptaAskIITians Faculty
```
6 years ago Arun Kumar
IIT Delhi
256 Points
```							HiThanks & Regards, Arun Kumar, Btech,IIT Delhi, Askiitians Faculty
```
6 years ago
Think You Can Provide A Better Answer ?

## Other Related Questions on Differential Calculus

View all Questions »  ### Course Features

• 731 Video Lectures
• Revision Notes
• Previous Year Papers
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Test paper with Video Solution  ### Course Features

• 51 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions