![davestrider404](/avatars/18409.jpg)
davestrider404
26.10.2019 •
Mathematics
Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius r.
Solved
Show answers
More tips
- C Computers and Internet How to Reinstall Windows: A Detailed Guide for Beginners...
- S Style and Beauty How to Get Rid of a Bruise: Tips and Tricks...
- F Food and Cooking Лечо: вкусное и простое блюдо для любой кухни...
- H Health and Medicine Relieving Swelling in Legs: Causes and Ways to Alleviate the Symptom...
Answers on questions: Mathematics
- M Mathematics Which equation is true for x=-6 and x=2...
- B Biology What antibiotic is recommended for use against gram negative bacteria?...
- C Computers and Technology Which of these are not referenced in an assembly? assemblies, sketches, part studios, surfaces, or plants...
- M Mathematics steven just deposited $10,000 in a bank account that has a 12 percent nominal interest rate, and the interest is compounded monthly. steven also plans to contribute...
- M Mathematics Which expression converts 4.5 gallons to quarts? A. 4.5 gal + 1 gal/4 qt B. 4.5 gal x 4 qt/1 gal C. 4.5 gal x 1 gal/4 qt D. 4.5 gal x 4 gal/1 qt...
Ответ:
Step-by-step explanation:
Given that a rectangle is inscribed in a circle of radius r.
Since diameter subtends right angle at the circumference we get diagonal of the rectangle is diameter of the circle
Let l and w be the dimensions
Then![l^2+w^2 = 4r^2](/tpl/images/0347/2209/3dcd7.png)
Hence A =lw maximum when A square is maximum
i.e.![A^2=l^2 w^2 = l^2 (4r^2-l^2)\\= 4r^2l^2 -l^4\\](/tpl/images/0347/2209/abda7.png)
Use derivative test
I derivative =![8r^2l-4l^3=0\\l=0 or l = \sqrt{2} r](/tpl/images/0347/2209/750d2.png)
II derivative <0 for non zero value of l
Hence maximum when![l=\sqrt{2} r\\w=\sqrt{2} r](/tpl/images/0347/2209/55a28.png)
Or rectangle is a square with equal sides
Ответ: