ACT Math : How to find the length of the diagonal of a square
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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:
Example Question #143 : Quadrilaterals
What is the area of a square with a diagonal of length 
Based on the data provided, the square could be drawn like this:
Based on this, you can use the Pythagorean theorem to find 
From this, you know that
Since the area is equal to 
Example Question #3 : How To Find The Length Of The Diagonal Of A Square
The perimeter of a square is 
From the perimeter, we can find the length of each side of the square. The side lengths of a square are equal by definition therefore, the perimeter can be rewritten as,
Then we use the Pythagorean Theorme to find the diagonal, which is the hypotenuse of a right triangle with each leg being a side of the square.
Example Question #1 : Squares
Find the diagonal of a square with side length 
To solve, simply realize the triangle that is made by 
Example Question #2 : Squares
Find the length of a diagonal of a square whose side length is 
To solve, simply remember that the diagonal forms an isoceles right triangle. Thus, the diagonal is:
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