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 2 years ago
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
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.

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

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

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

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

Zekarias
 2 years ago
Best ResponseYou've already chosen the best response.1consider 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.

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

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

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.112/y = 20/x y = (3/5)x

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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