Math CentralQuandaries & Queries


Question from roxanne, a teacher:

the dimensions of the rectangle: 3x length and 4x width. What is the area of the rectangle in square units?

Hi Roxanne,

There is some number x which you don't know but you are being told that the rectangle is 3 times x units long and 4 times x units wide. The area of a rectangle is its length times its width so the area of this rectangle is

(3 times x) times (4 times x) square units.

If I use the × symbol for multiplication this is

(3 × x) × (4 × x) square units.

3 × 4 = 12 and x × x can be written x2 and hence the area of the rectangle can be written

12 × x2 square units.

Many times in algebraic notation we don't write the × for multiplication, we just write the quantities to be multiplied adjacent to each other. Thus I might write the area of the rectangle

12x2 square units.

I hope this helps,

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