High School Math : How to find the length of the diagonal of a square
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Example Questions
Example Question #1 : Squares
What is the length of a diagonal of a square with a side length 
A square is comprised of two 45-45-90 right triangles. The hypotenuse of a 45-45-90 right triangle follows the rule below, where 
In this instance, 
Example Question #583 : High School Math
A square has sides of 
To find the diagonal of the square, we effectively cut the square into two 
The pattern for the sides of a 
Since two sides are equal to 
Therefore, the diagonal (the hypotenuse) will have a length of 
Example Question #584 : High School Math
A square has sides of 
To find the diagonal of the square, we effectively cut the square into two 
The pattern for the sides of a 
Since two sides are equal to 
Therefore, the diagonal (the hypotenuse) will have a length of 
Example Question #231 : Geometry
What is the length of the diagonal of a square with a side length of 
To find the diagonal of a square, we must use the side length to create a 90 degree triangle with side lengths of 
Pythagorean’s Theorem states 
Take 
After squaring the numbers, add them together:
Once you have the sum, take the square root of both sides:
Simplify to find the answer: 
Example Question #1 : How To Find The Length Of The Diagonal Of A Square
What is the length of the diagonal of a 7-by-7 square? (Round to the nearest tenth.)
To find the diagonal of a square we must use the side lengths to create a 90 degree triangle with side lengths of 7 and a hypotenuse which is equal to the diagonal.
We can use the Pythagorean Theorem here to solve for the hypotenuse of a right triangle.
The Pythagorean Theorem states
Plug the side lengths into the equation as 
Square the numbers:
Add the terms on the left side of the equation together:
Take the square root of both sides:
Therefore the length of the diagonal is 9.9.
Example Question #6 : How To Find The Length Of The Diagonal Of A Square
The perimeter of a square is 48. What is the length of its diagonal?
Perimeter = side * 4
48 = side * 4
Side = 12
We can break up the square into two equal right triangles. The diagonal of the sqaure is then the hypotenuse of these two triangles.
Therefore, we can use the Pythagorean Theorem to solve for the diagonal:
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