Determine the dimensions of a square-shaped chessboard having an area of eighty-one square centimeters.
Now let’s think. The definition of a square is that its length is the same as it’s width. So this distance is the same as this distance. And the area of a rectangle or a square is the length times width. And in this case obviously, the length and the width are both the same; they’re both 𝑥.
And the question tells us that the area is eighty-one square centimeters. So eighty-one is equal to 𝑥 times 𝑥. Well 𝑥 times 𝑥 is 𝑥 squared. But we want to know what 𝑥 is, so that we can work out the dimensions of this square. So we’re gonna need to take the square root of both sides. So on the left-hand side, we’re gonna have the square root of eighty-one and on the right-hand side, we’re gonna have the square root of 𝑥 squared, which is just 𝑥. Now the square root of eighty-one is nine. So 𝑥 is equal to nine.
Well if you wanted to be really picky, if we look back to this line here, we’re saying 𝑥 squared is equal to eighty-one. So yep, 𝑥 equals nine is a perfectly good solution. But also 𝑥 equals negative nine would work as well, because negative nine times negative nine is also eighty-one. But because 𝑥 is representing a physical length, we’re going to ignore this negative value. We’re not going to have negative lengths in real life.
So now we’re in a position to write down the dimensions of our square-shaped chessboard, and we need to think about the units as well. Remember, the area was in square centimeters, so our lengths are just in centimeters.
So the answer is: Our chessboard is nine centimeters by nine centimeters.