15. A rectangular garden is surrounded by a path of constant width. The perimeter of the garden is $24 \mathrm{~m}$ shorter than the distance along the outside edge of the path. What is the width of the path?
A $1 \mathrm{~m}$
B $2 \mathrm{~m}$
C $3 \mathrm{~m}$
D $4 \mathrm{~m}$
E $5 \mathrm{~m}$
15. C Let the length and width of the garden be $a$ metres and $b$ metres respectively and let the width of the path be $x$ metres. The perimeter of the garden is $2(a+b)$ metres and the perimeter of the larger rectangle formed by the garden and the path is $2(a+2 x+b+2 x)$ metres. Hence the difference between the distance along the outside edge of the path and the perimeter of the garden in metres is $2(a+2 x+b+2 x)-2(a+b)=8 x$. Therefore $8 x=24$ which has solution $x=3$. Hence the width of the path is 3 metres.