How do we find the diagonal of a square when given the area? We'll solve this geometry problem in today's video math lesson!
This is a fairly straightforward problem, and unsurprisingly it requires us to use the Pythagorean theorem! If we have a square that has area 25, for example, we know the side lengths of the square are the square root of 25 - since the area is the side length squared. Thus the square has sides of length 5. Two sides of a square that intersect in a right angle can then be treated as the leg lengths of a right triangle formed by those sides with the diagonal of a square (the video will make this more clear with a diagram). To finish solving the problem we just apply the Pythagorean theorem to find the diagonal length of the square, which is the hypotenuse of our right triangle!
We could use this method to create a general formula (the formula would be, given an area A of a square, the diagonal d is d = sqrt(2A) ). But I'd recommend just solving the problem whenever necessary, rather than memorizing a formula, because it is a quick problem to solve once you know how to do it.
Note that this method doesn't work for rectangles in general since a rectangle may not have sides of equal lengths. For example, if a rectangle had an area of 6, it could have sides of 3 and 2 or 6 and 1, just to name two possibilities. But a square with area 6 must have sides of length sqrt(6).
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I hope you find this video helpful, and be sure to ask any questions down in the comments!
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31 июл 2024
