Question

The area of a rectangular field is the product of its length and width. If each dimension of the rectangular field is multiplied by 3, then the area of the enlarged field is how many times the area of the original field?

Answer 1

Step 1

The area of the rectangular field is given as;

`A=\text{length(l)}* width(w)=lw`

If the dimensions of the field are multiplied by 3, then we will have;

`\begin{gathered} 3(\text{length)}=3l \\ 3(\text{width)}=3w \end{gathered}`

Step 2

Find by how many times the area of the enlarged field is bigger than the area of the original field.

`\begin{gathered} \text{Area of enlarged field= 3}l*3w=9lw \\ \text{Number of times the enlarged field is bigger=}(9lw)/(lw)=9 \end{gathered}`

Therefore the area of the enlarged field is 9 times the area of the original field.