The sides of a fish tank are 14 inches long. What is the distance between opposite corners of the fish tank? Round your answer to the nearest inch.
Pythagorean Theorem:
a^2 + b^2 = c^2
14^2 + 14^2 = c^2
196 + 196 = c^2
392 = c^2
19.799 = c
To find the distance between opposite corners of the fish tank, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the two sides of the fish tank form the two legs of a right triangle, and we want to find the length of the hypotenuse (the distance between opposite corners).
Using the Pythagorean theorem, we have:
Hypotenuse^2 = Side1^2 + Side2^2
Let's substitute the given length of the sides into the equation:
Hypotenuse^2 = 14^2 + 14^2
Hypotenuse^2 = 196 + 196
Hypotenuse^2 = 392
To find the length of the hypotenuse (distance between opposite corners), we need to take the square root of both sides of the equation:
Hypotenuse = √392
Using a calculator, we find that √392 is approximately 19.8.
Rounding to the nearest inch, the distance between opposite corners of the fish tank is approximately 20 inches.