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hawkfalcon
Group Title
The height of triangle ACE is 12 and base AE = 20. A rectangle is inscribed in triangle ACE as shown below.?
a) Express the rectangle’s area as a
function of x and y.
Use the fact that the triangle ACE is
similar to triangle BCD to write y as a
function of x.
c)Express the rectangle’s area as a function of only x.
d) Find the maximum possible area of the rectangle.
 2 years ago
 2 years ago
hawkfalcon Group Title
The height of triangle ACE is 12 and base AE = 20. A rectangle is inscribed in triangle ACE as shown below.? a) Express the rectangle’s area as a function of x and y. Use the fact that the triangle ACE is similar to triangle BCD to write y as a function of x. c)Express the rectangle’s area as a function of only x. d) Find the maximum possible area of the rectangle.
 2 years ago
 2 years ago

This Question is Closed

hawkfalcon Group TitleBest ResponseYou've already chosen the best response.0
dw:1345995812545:dw
 2 years ago

hawkfalcon Group TitleBest ResponseYou've already chosen the best response.0
Nobody knows what to do?:#
 2 years ago

hawkfalcon Group TitleBest ResponseYou've already chosen the best response.0
@Zekarias ?
 2 years ago

Zekarias Group TitleBest ResponseYou've already chosen the best response.1
a) (12y)x b) 12(x0.1x^2) c) 30 sq units
 2 years ago

Zekarias Group TitleBest ResponseYou've already chosen the best response.1
Is "How" for all of it?
 2 years ago

hawkfalcon Group TitleBest ResponseYou've already chosen the best response.0
Just b and c
 2 years ago

hawkfalcon Group TitleBest ResponseYou've already chosen the best response.0
especially b... :O
 2 years ago

Zekarias Group TitleBest ResponseYou've already chosen the best response.1
consider the perpendicular line form C, we can come out with the ratio 12/y =10/x, where 10 is half the rectangles side,20. Then simplify it so as to inset the result in to the equation in 'a'. To 'c' just use the application of derivative.
 2 years ago

hawkfalcon Group TitleBest ResponseYou've already chosen the best response.0
Okay. Makes sense I guess:p thanks!
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
small catch
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
triangle ACE is similar to triangle BCD => height1/height2 = base1/base2
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
12/y = 20/x y = (3/5)x
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
this would give you max area 60
 2 years ago

hawkfalcon Group TitleBest ResponseYou've already chosen the best response.0
o.O But y needs to be written as a function of x.
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
y = (3/5)x
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
its a function of x
 2 years ago

hawkfalcon Group TitleBest ResponseYou've already chosen the best response.0
Oh yeah :3. So why did you use the entire base and @Zekarias used 1/2?
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
since both are similar triangles, "ratio of bases" equals "ratio of heights"
 2 years ago

hawkfalcon Group TitleBest ResponseYou've already chosen the best response.0
Okay, that makes sense. :3 Can you explain how you got 60 though?
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
write the area equation in x and optimize
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
for optimizing, use either of the below two : 1) its a parabola facing down so max value = f(b/2a) or 2) use calculus
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
this q from conics, or calculus ?
 2 years ago

hawkfalcon Group TitleBest ResponseYou've already chosen the best response.0
calculus. Going into calculus next year and they gave us some prep stuff*.*
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
oh ok, so we have this so far : A = x(12y) (1) y = (3/5)x (2)
 2 years ago

hawkfalcon Group TitleBest ResponseYou've already chosen the best response.0
Okay, true.
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
hmm which one moves ?
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
ohhk yeah as we go down its moving a lot it seems...
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
substitute (2) in (1)
 2 years ago

hawkfalcon Group TitleBest ResponseYou've already chosen the best response.0
x(12(3/5)x)
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
\(A = x(12  \frac{3}{5}x)\) \(A = 12x \frac{3}{5}x^2)\)
 2 years ago

hawkfalcon Group TitleBest ResponseYou've already chosen the best response.0
Okayy and solve for x
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
nope we need to optimize A
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
find maximum possible value of A, right ?
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
theres a process for finding maximum/minimum values of any funcitons
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
you familiar with differentiation ?
 2 years ago

hawkfalcon Group TitleBest ResponseYou've already chosen the best response.0
... I guess I havenet learned that yet..
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
its simple... if you knw differentiation already
 2 years ago

hawkfalcon Group TitleBest ResponseYou've already chosen the best response.0
I think we are learning that next year :( (monday)
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
just if you knw derivative of x, and x^2, its enough
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
oh ok then you cannot use calculus, lets switch to conics. you knw parabolas, right
 2 years ago

hawkfalcon Group TitleBest ResponseYou've already chosen the best response.0
Okay, I don't know how to do that.. Maybe I should make a new question asking for the dirivative of A=12x3/4x^2
 2 years ago

hawkfalcon Group TitleBest ResponseYou've already chosen the best response.0
You said f(b/2a)
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
A = 12x  (3/5) x^2
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
\(A = \frac{3}{5}x^2 + 12x\)
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
a = 3/5 b = 12
 2 years ago

hawkfalcon Group TitleBest ResponseYou've already chosen the best response.0
Cool, thanks, just plug and chug now:D
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
f(b/2a) gives the vertex y coordinate, which is the maximum value
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
dw:1345999525420:dw
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
b/2a = 10 f(b/2a) = ?
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
put x = b/2a = 10, in area function
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
if you remember, for any parabola, b/2a is the xcoordinate of vertex f(b/2a) is the ycoordinate of vertex
 2 years ago

hawkfalcon Group TitleBest ResponseYou've already chosen the best response.0
Thank you so much! Now I can do the rest of these problems:D
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
glad to hear ! calculus wud be much fun :) good luck !!
 2 years ago
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