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Area of a square is 6.25 cm (square).  Find each side of the square in mm.

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umaa | Student, Grade 9 | (Level 1) Honors

Posted February 3, 2009 at 7:22 PM via web

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Area of a square is 6.25 cm (square).  Find each side of the square in mm.

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frizzyperm | College Teacher | (Level 1) Educator

Posted February 3, 2009 at 8:04 PM (Answer #1)

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You have mixed units... lets make every thing millimeters. So the area of your square is 625 sq. mm.

A square has 4 equal sides, lets call these equal sides length A. 

and the formula to find the area of a square is

area of a square = sidelength squared.


625 sq mm = A^2

so... what number when squared equals 625?

or, the same problem reversed is ... what is the square root of 625?

I'll leave you to finish that.


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cburr | Middle School Teacher | (Level 2) Associate Educator

Posted February 4, 2009 at 7:16 AM (Answer #2)

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I thought it might be useful to explain to you why 6.25 cm^2 is the same as 625 mm^2.

One centimeter is equal to 10 millimeters.  However, we are talking about square centimeters and millimeters.  Imagine you have a square which is 1 cm on each side, so it is 1 cm^2.  If you change that 1 cm to 10 mm, then the square is 10mm on each side.  That means the area is 10 x 10, or 100 mm^2.  If you picture this square, you can see it.  The bottom of the square is cut into one row of 10 little mm squares.  But, there are 10 rows going up the side.  So, there are a total of 100 little mm squares.

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revolution | College Teacher | (Level 1) Valedictorian

Posted September 9, 2010 at 6:06 PM (Answer #3)

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1cm=10mm (metric conversion)

1cm^2= 10^2mm= 100mm^2

So for 6.25cm^2= 100*6.25= 625mm^2

To get the length of each side of square, you need to square root the area of the square which is:

length of one side = sqrt625= 25mm


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atyourservice | Student, Grade 11 | TA | (Level 3) Valedictorian

Posted May 29, 2014 at 11:23 PM (Answer #4)

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Area of a square is 6.25 cm (square).  Find each side of the square in mm.

The area of a square is length x width and they are the same numbers so just convert the cm into mm and then find the square root of that number

1cm = 10mm^2 = 100 mm

6.25 x 100 = 625 mm

 `sqrt(625)` = 25 mm

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tonys538 | Student, Undergraduate | TA | (Level 1) Valedictorian

Posted September 27, 2014 at 5:30 AM (Answer #5)

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The area of a square with sides of length a is given by A = a^2.

In the problem, the square has area 6.25 cm^2, 6.25cm^2 = 6.25*10*10 = 625 mm^2

If the sides of the square have length a, `a^2 = 625` , a = `sqrt 625` = 25

The length of the sides of the square is 25 mm or 2.5 cm

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