Top Posters
Since Sunday
a
5
k
5
c
5
B
5
l
5
C
4
s
4
a
4
t
4
i
4
r
4
r
4
Home Q & A Board Science-Related Homework Help Mathematics
New Topic  
juelz juelz
wrote...
Go to Answer
Posts: 28
Rep: 0 0
11 years ago
The legs of the triangle are 3cm and 4cm and two sides of the rectangle lie along the legs.

This is an optimization problem where I need to maximize the area of the rectangle.  My problem here is finding a way to get the area of the rectangle in terms of one variable.

Using common sense, I do know that the area of the triangle is 6 cm^2 and the area of the rectangle must be smaller than this.
Read 516 times
4 Replies
Replies
Answer accepted by topic starter
smartgirlsmartgirl
wrote...
#1
Posts: 3
Rep: 0 0
11 years ago
Sign in or Sign up in seconds to unlock everything for free
1

Related Topics

wrote...
#2
11 years ago
Okay, imagine it set up on a coordinate system.
Then we know that y/x=4/3.
And the area of rectangle is (3-x)y = (3-x)(4x/3)
=4x-4x^2/3
Now diiferinate and set to 0, giving you
4-8x/3=0, or 4=8x/3.
So, x=12/8=3/2.
SO, the area is (3-3/2)((4/3)(3/2)) = (3/2)(2)
=3. SO, maximum area is 3.
wrote...
#3
11 years ago
Use similar triangles.  x/(3-y)=4/3

y=3-(3x/4)

Area of rectangle is xy

A=x(3-(3x/4))

A'=3-3x/2

3-3x/2=0

x=2 and y=3/2
wrote...
#4
11 years ago
2*1
New Topic      
Quick Reply
Explore
Post your homework questions and get free online help from our incredible volunteers
  1155 People Browsing
Start New Topic Take the Tour CoursesNew Study Tools Topics Trending Browse by Textbook
Live Chat
Related Images
  
 1118
  
 288
  
 332
Your Opinion
Which industry do you think artificial intelligence (AI) will impact the most?
Votes: 352
Previous poll results: What percentage of nature vs. nurture dictates human intelligence?