Expert: Josh - 8/26/2008

Question
find the approximate length of the side of a square whose area is equal to the area of a rectangle with sides 160m and 1.6m

Answer
Hi Iris

The best way for me to help is that you attempt this problem yourself, then let me know where you are stuck. Have you looked at similar problems you have done in class or something from the textbook?

There is one thing you need to know for this question.
1) The formula for the area of a rectangle is A(rect)=w*h, where w and h represent the width and height, respectively.

The expression for the area of a square follows from this. By definition, all sides in a square have equal length. So, w is the same as h. Thus, the area of a square is A(square)=w*w.

We were told the rectangle has dimensions 160m by 1.6m. It doesn't matter which one we call "w", which one we call "h"; it makes no difference to the area.

Let's say w=160, h=1.6. Using a calculator, work out the product w*h. This number, let's call this A(rect), is the area of the rectangle.

If the square has the same area, then, A(square)=A(rect)=w*w. Remember that A(rect) is just a number (160*1.6) at this stage.

So, taking the square root on both sides of the equation, the length is given by w=square_root(160*1.6).