How to find the length of the diagonal of a square - ACT Math
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The perimeter of a square is 48. What is the length of its diagonal?
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:
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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The perimeter of a square is 
units. How many units long is the diagonal of the 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.
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.
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What is the area of a square with a diagonal of length 
? Round to the nearest hundredth.
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 
:
or 
From this, you know that 
Since the area is equal to 
, this is your answer!
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
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Find the diagonal of a square with side length 
.
Find the diagonal of a square with side length
To solve, simply realize the triangle that is made by 
sides and the diagonal is an isoceles right triangle. Thus, the hypotenuse is side length time square root of 
. Thus,
To solve, simply realize the triangle that is made by
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Find the length of a diagonal of a square whose side length is 
.
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:
To solve, simply remember that the diagonal forms an isoceles right triangle. Thus, the diagonal is:
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