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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.
 one year ago
 one year 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.
 one year ago
 one year ago

This Question is Closed

hawkfalconBest ResponseYou've already chosen the best response.0
dw:1345995812545:dw
 one year ago

hawkfalconBest ResponseYou've already chosen the best response.0
Nobody knows what to do?:#
 one year ago

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

ZekariasBest ResponseYou've already chosen the best response.1
Is "How" for all of it?
 one year ago

ZekariasBest 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.
 one year ago

hawkfalconBest ResponseYou've already chosen the best response.0
Okay. Makes sense I guess:p thanks!
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.1
triangle ACE is similar to triangle BCD => height1/height2 = base1/base2
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.1
12/y = 20/x y = (3/5)x
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.1
this would give you max area 60
 one year ago

hawkfalconBest ResponseYou've already chosen the best response.0
o.O But y needs to be written as a function of x.
 one year ago

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

ganeshie8Best ResponseYou've already chosen the best response.1
since both are similar triangles, "ratio of bases" equals "ratio of heights"
 one year ago

hawkfalconBest ResponseYou've already chosen the best response.0
Okay, that makes sense. :3 Can you explain how you got 60 though?
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.1
write the area equation in x and optimize
 one year ago

ganeshie8Best 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
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.1
this q from conics, or calculus ?
 one year ago

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

ganeshie8Best 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)
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.1
hmm which one moves ?
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.1
ohhk yeah as we go down its moving a lot it seems...
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.1
substitute (2) in (1)
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.1
\(A = x(12  \frac{3}{5}x)\) \(A = 12x \frac{3}{5}x^2)\)
 one year ago

hawkfalconBest ResponseYou've already chosen the best response.0
Okayy and solve for x
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.1
nope we need to optimize A
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.1
find maximum possible value of A, right ?
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.1
theres a process for finding maximum/minimum values of any funcitons
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.1
you familiar with differentiation ?
 one year ago

hawkfalconBest ResponseYou've already chosen the best response.0
... I guess I havenet learned that yet..
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.1
its simple... if you knw differentiation already
 one year ago

hawkfalconBest ResponseYou've already chosen the best response.0
I think we are learning that next year :( (monday)
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.1
just if you knw derivative of x, and x^2, its enough
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.1
oh ok then you cannot use calculus, lets switch to conics. you knw parabolas, right
 one year ago

hawkfalconBest 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
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.1
\(A = \frac{3}{5}x^2 + 12x\)
 one year ago

hawkfalconBest ResponseYou've already chosen the best response.0
Cool, thanks, just plug and chug now:D
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.1
f(b/2a) gives the vertex y coordinate, which is the maximum value
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.1
dw:1345999525420:dw
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.1
b/2a = 10 f(b/2a) = ?
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.1
put x = b/2a = 10, in area function
 one year ago

ganeshie8Best 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
 one year ago

hawkfalconBest ResponseYou've already chosen the best response.0
Thank you so much! Now I can do the rest of these problems:D
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.1
glad to hear ! calculus wud be much fun :) good luck !!
 one year ago
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