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The length of diagonal of a square measure 10cm^2. What is the perimeter of the square? Express your answer in simplest radical form.

 Jan 23, 2019
 #1
avatar+107405 
+1

The side of the square =    10 / √2   cm   =  5√2 cm

 

And the perimeter is  4 times this  =  20√2 cm

 

 

cool cool cool

 Jan 23, 2019
 #2
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Where did you get the radical 2 from?

Guest Jan 23, 2019
 #4
avatar+107405 
+1

Note that we can use the Pythagorean Theorem to find the diagonasl of a square

 

diagonal  =  sqrt (side^2 + side^2)  =  sqrt ( 2 * side^2)  =  side * sqrt (2)

 

So....the side =   diagonal /  sqrt (2)

 

So we have that the side =  10 / sqrt (2)

 

Multiply top/bottom by sqrt (2)   and we get that

 

side  =  10 sqrt (2) / [ sqrt (2) * sqrt (2) ]  =  10 sqrt (2) / 2   =  5 sqrt (2)

 

 

cool cool cool

CPhill  Jan 23, 2019
 #3
avatar+1035 
-1

We know a square has all 90 degree angles and equivalent side lengths, and the diagonal is \(10\sqrt2\).

So, you could make a right triangle, with two of the sides and the diagonal!

\(x^2+x^2=(10\sqrt2)^2\) so \(2x^2=200, x^2=100, x=10\)because x cannot be negative.

This is the side length of the square, so now just multiply it by four to get 40 cm.

 

You are very welcome!

:P

 Jan 23, 2019

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