For the square with side length n, the diagonal measures:
The sidelength of the square is n, and we want to get the length of the diagonal d.
Notice that the diagonal is the hypotenuse of a right triangle whose catheti measure n.
Then we can use the Pythagorean theorem, which says that the square of the hypotenuse is equal to the sum of the squares of the cathetus;
That is the length of the diagonal.
If you want to learn more about right triangles:
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We have been given that a plane takes off from the New Orleans airport and flies over the Gulf at 1,500 ft. Above sea level. At the same time a submarine leaves the port in New Orleans, submerges and travels at 300 feet below sea level. We are asked to find the distance between the plane and the submarine.
Since the airplane is above sea level, so elevation of plane will be positive that is .
Since the submarine is below sea level, so elevation of submarine will be negative that is .
Now we can find distance between the plane and the submarine as:
Therefore, the distance between the plane and the submarine is 1800 feet.