Math CentralQuandaries & Queries


Question from daniel, a student:

a square field has an area of 289 meter squared. How do you calculate the dimensions

Hi Daniel. Remember that the area of a square is the length of its side

That means that a square with dimensions of 3m by 3m would have an area
of 32 = 9 square meters.

Similarly, a 4m by 4m square would have an area of 42 = 16 square meters.

So to go the other way, you do the inverse of squaring the number. That
means you take the square root.

For example, a square with an area of 25 square meters would have sides
of length √25 = 5 meters.

The square root of 36 is 6, so an square with area of 36 would have
sides of length 6.

Now using this idea, what are the dimensions of a square with an area of
289 square meters?

Hope this helps,
Stephen La Rocque.


Hi Daniel,

Since the field is a square each of the sides is of the same length. Suppose this length is s meters. The area of the square is then s × s = s2 square meters. But you know that the area is 289 square meters. Thus

s2 = 289 square meters.

Solve for s,

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