Question

To convert from ft² to yd², you should

(a) multiply by 3.

(b) multiply by 1/3.

(c) multiply by 9.

(d) multiply by 1/9.

(e) multiply by 6.

(f) multiply by 1/6.

Short answer

The correct option is (d).

Step-by-step solution

Relation between yd and ft

The conversion of a unit is a process in which the unit of the measurement of a quantity changes from one prospect to another. There is a set factor by which the particular quantity needs to be multiplied or divided for every conversion.

You know that the relation between ft and yd is

\(\begin{aligned}{c}1\,\,{\rm{yd}} = 3\,\,{\rm{ft}}\\1\,\,{\rm{ft}} = \frac{1}{3}\,\,{\rm{yd}}\end{aligned}\).

Conversion of ft2 to yd2

Now,

\(\begin{aligned}{c}{\left( {1\,\,{\rm{ft}}} \right)^2} = {\left( {\frac{1}{3}\,\,{\rm{yd}}} \right)^2}\\1\,\,{\rm{f}}{{\rm{t}}^2} = \frac{1}{9}\,\,{\rm{y}}{{\rm{d}}^2}\\{\rm{f}}{{\rm{t}}^{\rm{2}}} = \frac{1}{9} \times {\rm{y}}{{\rm{d}}^2}\end{aligned}\)

Hence, to convert ft² to yd², the quantity must be multiplied by \(\frac{1}{9}\).