How would I find...

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

Dear dnntau,

Suppose the length of the field is "a" and the width is "b",

Area of the field; \(\displaystyle A=a\times{b}=ab\)----------1

If the lenght and the width is multiplied by 3,

Length=3a

Width=3b

Area; \(\displaystyle A'=3a\times{3b}=9ab\)--------2

By 1 and 2;

\(\displaystyle A'=9A\)

Therefore the area of the new field is "nine" times that of the original field.