Question

An area rug has a central 5 m by 3 m rectangle in a mosaic pattern, with a plain border of
uniform width around it. The total area of the rug is 24 square metres. Find the width of the
border.

Answer 1

Assuming the “central” part means the rug without its border, you can subtract the central portion from the total area of the rug & border, and you’ll have your area of the border.

\(\sf{A_{border} = 24 - ( 5 \times 3 )}\)

Answer 2

It's asking for the width of the border, which makes the calculation a bit more involved.



the border of the 3*5 rectangle has a uniform width. let's call that width x.

therefore, the width of the entire rectangle is 3 + x + x, or simply 3 + 2x

same logic with the length, 5 + 2x

the area of the whole rectangle is 24, so 24 = (3 + 2x)(5 + 2x), solve for x.