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**scubasteve94** A rectangle ABCO has two vertices, C and B, on the x-axis and y-axis respectively and another vertex, A, on the graph of 2x+y=4, as shown in the diagram. the coordinates of A is (a,b) where a and b are positive real numbers.

i) find the area, R, of rectangle ABCO in terms of a.

ii) What is the possible value(s) of a, so that the rectangle ABCO exists?

iii) Sketch the graph of R.

iv) Find the maximum value of R and the value of a for which this occurs.

IF I WERE TO DO IT I WOULD:

i) R = 2aX2b

$\displaystyle R = a(4 - 2a)$

ii) possible value(s) of a = ≤1

$\displaystyle 0 < a < 2$

iii) Unsure how to this part?

$\displaystyle R = x(4-2x)$ **... graph is an inverted parabola**

iv) i think it has to do with previous question so unsure again

**maximum value occurs at the vertex of the parabola **