I was wondering how I had to solve this question?
The maximum side length of the rectangle is $10$m. L: $(x+4)$, W: $(x-1)$
a) Write a function which gives perimeter, $P$ metres, of the rectangle.
b) State the domain and range of this function.
I tried approaching it from $10-x-4$, which would give me $6-x$ for length. Then $10-x+1$, which would give me $11-x$ for width. But, that wouldn't make sense since the width is suddenly bigger.
So I tried $10-x+4$, which would give me $14-x$ and $10-x-1$, which would give me $9-x$. This would mean that the perimeter is $46-4x$, and my domain will be $[1.5,9]$. Is this correct?
Thanks.
a) $$P=2L+2W = 2(x+4)+2(x-1) = 4x+6$$
b) Domain is $$1<x\le 6$$
Range is $$ 10<P\le 30$$