High School Math : How to find the length of the diagonal of a square
Study concepts, example questions & explanations for High School Math
All High School Math Resources
Example Questions
Example Question #1 :Squares
长度是什么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 #2 :Squares
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 #3 :Squares
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 #1 :How To Find The Length Of The Diagonal Of A Square
长度是什么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 :Squares
长度是什么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:
Certified Tutor
All High School Math Resources
