Re: Can someone show me the working for this please

On Wed, 29 Aug 2007 14:31:51 -0000, Dougsd1r <dougsdir@xxxxxxxxx>
wrote:

A rectangular based area is fenced using 40m of fencing

Taking x metres for its length, show that the area of the rectangle,
A m^2, can be written

A = 100 - (x - 10)^2 . What is the maximum floor area, and the
corresponding length and breadth.

I know the answer is A=100m^2 , length = 10m, breadth = 10m

This question is in relation to questions on quadratic function f(x) =
ax^2+bc+c i have been doing

TIA

Let the rectangle have perimeter P, length x, and width y. Then

P = 2x + 2y, so P/2 = x + y, and (P/2 - x) = y

The area is

A = xy = x (P/2 - x)

A = -x^2 + P/2 x

By completing the square, show that

A = P^2/16 - (x - P/4)^2

The area A will be maximum when x equals what particular value?

For any rectangle with fixed perimeter P, what shape has maximum area?

.