how to find side length of square from diagonal

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The diagonal of a square is the line stretching from one corner of the square to the opposite corner. To find the diagonal of a foursquare, you can use the formula ${\displaystyle d=s{\sqrt {2}}}$ , where ${\displaystyle southward}$ equals one side length of the square. Sometimes, however, you might exist asked to observe the length of the diagonal given another value, such as the perimeter or area of the foursquare. In these instances information technology is necessary to use unlike formulas first, so that yous tin determine the side length before using the diagonal formula.

1. i

   Detect the length of one side of the square. This volition probably be given to yous. If you lot are working with a foursquare in the real world, use a ruler or piece of measuring tape to detect the length. Since all four sides of the square are the aforementioned length, you can apply whatsoever side of the square. If y'all exercise not know the length of ane side of the foursquare, you cannot use this method.

   • For example, you might want to find the length of the diagonal of a square that has sides 5 centimeters long.

2. ii

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3. iii

   Plug the side length of the square into the formula. Make certain yous are substituting for the variable ${\displaystyle s}$ .

   • For example, if the foursquare has a side length of 5 centimeters, set up the formula like this:
     ${\displaystyle d=5{\sqrt {2}}}$

4. iv

   Multiply the length of the side past $$ 2 {\displaystyle {\sqrt {2}}} . This will give y'all the length of the diagonal. It'south best to perform the calculation on a computer, so that you tin get a more precise result. If you don't have a estimator, yous tin round ${\displaystyle {\sqrt {two}}}$ to 1.414.

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1. ane

2. 2

   Plug the length of the perimeter into the formula. Brand sure y'all are substituting for the variable ${\displaystyle P}$ .

   • For example, if the perimeter of the square is 20 centimeters, your formula will look like this:
     ${\displaystyle twenty=4s}$

3. 3

   Solve for $$ south {\displaystyle s} . To do this, carve up each side of the equation by 4. This will give you the length of one side of the foursquare.

4. 4

5. five

   Plug the side length of the square into the formula. Make sure you are substituting for the variable ${\displaystyle s}$ .

   • For example, if the square has a side length of 5 centimeters, fix upwardly the formula similar this:
     ${\displaystyle d=v{\sqrt {ii}}}$

6. half dozen

   Multiply the length of the side by $$ ii {\displaystyle {\sqrt {two}}} . This will requite you the length of the diagonal. It's best to perform the calculation on a figurer, so that you can get a more precise result. If y'all don't have a estimator, you lot tin round ${\displaystyle {\sqrt {ii}}}$ to 1.414.

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1. 1

2. 2

   Plug the expanse measurement into the formula. Make sure yous are substituting for the variable ${\displaystyle A}$ .

   • For example, if the surface area of the square is 25 square centimeters, your formula will expect like this:
     ${\displaystyle 25=s^{two}}$

3. 3

   Solve for $$ southward {\displaystyle south} . To do this, find the square root of the area. This volition give you the length of one side of the square. To observe the foursquare root, use a reckoner. If you need help calculating the square root by hand, read Calculate a Square Root by Paw.

4. 4

5. 5

   Plug the side length of the square into the formula. Brand sure you are substituting for the variable ${\displaystyle southward}$ .

   • For case, if the square has a side length of v centimeters, set up the formula similar this:
     ${\displaystyle d=five{\sqrt {ii}}}$

6. half dozen

   Multiply the length of the side by $$ 2 {\displaystyle {\sqrt {two}}} . This will requite you lot the length of the diagonal. *It'south best to perform the adding on a figurer, and then that you tin go a more precise result. If you don't take a calculator, y'all can circular ${\displaystyle {\sqrt {2}}}$ to 1.414.

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Add New Question

• Question

  How exercise I calculate the sides of a square if the diagonal is given?

  

  Outset square the diagonal's length. Divide that past two. And then find the square root of that terminal number. That's the side of the square.

• Question

  How do you find the diagonal of a 24 ten 24 foot square?

  

  Since you know the length of one side (24) you can use method ane: d = south x sqrt*2 d = 24 x i.414 d = 33.936

• Question

  How practice I identify a right angle?

  

  You lot'll know if an bending is right angle if it is 90 degrees.

• Question

  What is the diagonal of a 15 x 7 pes area?

  

  A 15 ten 7 pes area is not a foursquare. You lot tin even so detect the length of the diagonal by using the Pythagorean Theorem: xv^2 + 7^2 = c^2, where c is the length of the diagonal. Thus: 15^2 + 7^two = c^two 225 + 49 = c^2 274 = c^2 sqrt*274 = sqrt*c^2 16.55 = c

• Question

  Diagonal measurement of a 4 inch foursquare

  

  Since you know the length of ane side of the foursquare (4), you lot can use method one. d = due south x sqrt*2 d = iv 10 ane.414 d = five.565

• Question

  A square is 8 feet by eight feet. What is the diagonal distance from corner to corner?

  

  Since you know the length of one side (8 feet), you can apply method 1: d = s x sqrt*two d = eight x one.414 d = 11.312

• Question

  How practice I calculate the area of a square?

  

  Multiply the length by the width. If they merely give you lot the length or the width, multiply that same number by itself, (for example: the length is 5 in, 5*5=25in2). This process but works with squares. If the problem only gives you the area and the length or width, you lot divide the expanse by the length or width.

• Question

  How to find diagonals when I but take the area?

  

  Double the area. Then notice the square root of that number. That's the diagonal.

• Question

  How tin I observe the diagonal length of a square that is 213 meters by 200 meters?

  

  This is not a foursquare. Withal, you can however utilize Pythagorean'southward Theorem to find the length of the diagonal. Diagonal length = D = sq. root of (213^two + 200^2) = sq. root (45369 + 40000) = sq. root (85369) = 292.ii.

• Question

  How do I foursquare a number?

  

  Multiply information technology by itself. For example, half-dozen² = (6)(6) = 36.

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Commodity Summary X

To calculate a diagonal of a square, multiply the length of one of the foursquare's sides by the square root of 2. If you don't know the length of ane side, y'all tin can find it by plugging the foursquare's perimeter into the formula: perimeter = 4s, where s is the length of 1 side. If you lot don't know the perimeter, you tin nevertheless notice the length of one side by plugging the square'due south area into the formula: area = s^2, where s is the length of 1 side. For assistance solving these formulas, go on reading!

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Source: https://www.wikihow.com/Calculate-a-Diagonal-of-a-Square

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