1. ## Another Perimeter Problem

A quilt measuring 120 cm by 80 cm is made for Emma's cot. Borders are added to a central rectangular panel. The borders are the same width. What are the possible dimensions of the central panel?

Can someone please explain this question to me? All help is appreciated.

A quilt measuring 120 cm by 80 cm is made for Emma's cot. Borders are added to a central rectangular panel. The borders are the same width. What are the possible dimensions of the central panel?

Can someone please explain this question to me? All help is appreciated.
If the borders are x cm wide, then you have to subtract 2x from the overall dimensions (120 by 80) to get the dimensions of the central panel. In other words, the panel will measure (120 - 2x) cm by (80 - 2x) cm. The central panel has possible dimensions, then, between 120 cm by 80 cm, (if x = 0) and 40 cm by 0 cm (if x = 40), with the length of the panel always being 40 cm more than its width.

Say the border is $\displaystyle x$ then one side is $\displaystyle 120-2x$ and the other is $\displaystyle 80-2x$, so the area of the central rectangle would be given by $\displaystyle (120-2x)(80-2x)$
Oh. I just realised that because $\displaystyle 0<x<40$ the possible dimensions for the longer side would be between 40 and 120cm and for the shorter side it would be between 0cm and 80cm.