A 3m wide path runs around a rectangular court. The length is 1.5 times the width. The area of the path is 1596 square metres. What are the dimensions

Question

A path, 3 metres wide, runs around the outside edge of a rectangular court. The court is half as long again as it is wide. The area of the path is 1596 square metres. What are the dimensions of the court? I got the dimensions to be 173.33 recurring metres by 86.66 recurring metres. Is this correct?

Answer 1

Once you get the picture here the process is straightforward; let $x$ be the length of the court, so that $2x$ is the width. Then the path consists of two $3\times x$ rectangles along the length, two $3\times 2x$ rectangles along the width, and four $3\times 3$ squares for each corner. Thus the area of the path is $$ 6x+12x+16; $$ so we have $18x+36=1596$, giving $x=86.\overline{6}$ as you said.

Answer 2

You can quickly get the perimeter of the court by subtracting all the $3\times 3= 9 m^2$ corners from the area, $1596-36 = 1560 m^2$, then dividing by the width $1560/3=520m$ perimeter.

Then - here is your misunderstanding - the length is "half as much again", $1.5\times $ the width $w$, giving the perimeter $520=5w$ so $w=104m$ and the length $l = \frac 32w = 156m$.