Maxima Minia Problem (1 Viewer)

[cutemouse]

Hello,

Not sure if this belongs in 3U, but if someone could help me then that'd be great.

Here's the question:

Isoceles trapezia are drawn with side CD always 24cm, sides AD and BC equal and AD+AB+BC=42cm. Find the dimensions of the trapezium with greatest possible area.

Diagram is attached.

Thanks

 

[cutemouse]

No one can do this? I'm quite desperate.. haha

 

[Templar]

 

[gurmies]

I got same answer, but couldn't be stuffed posting up why h was equal to what it was...

 

[smp211]

Ok here is how to find h:

2x + y = 42
.:. y = 42 - 2x

we can see that the bottom 24 cm side minus the bits to the left and right is equal to y. (we will call each side "z")

.:. 42 - 2x = 24 - 2z
.:. 21 - x = 12 - z
.:. z = x - 9

now we have the base of the right angled triangle we are gonna use to find h.

using pythagoras' theorim,
x^2 = h^2 + (x - 9)^2
.:. h^2 = x^2 - (x^2 - 18x + 81)
.:. h^2 = 18x - 81
.:. h = (18x - 81)^1/2

bla bla bla
as the other guy said, you do all that, and get x = 14.

i wonder if this is a 3u question? it is very very easy after you realise how to find h.