Video: Finding the Side Length of a Square given Its Area

Calculate the side length of a square whose area is 6400 dm².

02:08

Video Transcript

Calculate the side length of a square whose area is 6400 decimeters squared.

We’re given the area of a square. We know that when we’re dealing with squares, the area equals side times side. We usually write that as side squared. If area is equal to a side length squared, we can plug in 6400 for the area, which will be equal to the side length of that square squared.

If we solve for 𝑥 [𝑠], we’ll find the side length. To do that, we need to get 𝑠 by itself. We currently have 𝑠 squared. If we take the square root of 𝑠 squared, we’ll be left with 𝑠. But if we take the square root of one side of the equation, we have to take the square root of the other side of the equation. We also need to take the square root of 6400. Of course at this point, if you were using a calculator, you would plug in the square root of 6400. But let’s consider the case where we don’t have a calculator.

I notice that 6400 is made up of two square factors, 64 and 100. The square root of 6400 is the same as multiplying the square root of 64 times the square root of 100. And we know that the square root of 64 is eight. And the square root of 100 is 10. The side length is going to be equal to eight times 10. The side length would be 80. Let’s go back and take a look at the units. The area is given as decimeters squared. And that means that the side length was measured in decimeters.

The side length of this square would be 80 decimeters.

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