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Find the square of the length of the diagonal of a square whose area is 16 cm2

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4 Answers

The answer below is totally wrong!! How can the diagonal have a greater magnitude than the Area. You solve it like this instead :

First find the length of each side of the square by:                                                                       √(Area)= Length of each side of square, which is √16 = 4 cm

Now divide the square into two isosceles right triangles with the diagonal.

Working on one of the triangles, apply Pythagorean Theorem i.e.

(Diagonal)2 = (4)2 + (4)2              the 4's come from the sides of the square that no form two equal sides of                       i                                             the isosceles right triangle

so (Diagonal)2 = 32

√(Diagonal)2 = √(32)

Diagonal= 4√2 cm   OR    

             ≈5.65685424949 cm          :-)

If a square has area 16 square cm, then each of its sides is 4. Use the Pythagorean theorem to find the diagonal of this square measures 4√2 cm. If you square 4√2 you get 32.

Answer if 32. 

Hmmm . . .  Let me venture to say that one of these other tutors is correct and the other is incorrect.  This word problem (like the ones found in the SAT Math section) is a case of reading comprehension -- reading the problem CAREFULLY!

Let's get started:  A square, by definition, has sides of all the same Length.  How do you find each Length?  Well, since the Area is found by A = L2   -----------> √A = L  ------------->  √16 = 4.  

 Something else you should know is that a square is essentially made up of 2 Right Triangles that share the same Diagonal.  Each of these Right Triangles is a 45°-45°-90° Triangle.  Now, if you memorized the Lengths of a 45°-45°-90° Triangle (and please do so), you will remember that the Hypothenuse is equal to L√2, when L represents the Length of each side (you can use any variable; You will often see this with "s" for Side).  

Hence, L√2 is both your Hypothenuse AND your Diagonal!  L=4, as we figured out above, so your Diagonal is 4√2.   But wait!!! You're not done!  The question asks for the Square of your Diagonal!

------------> (4√2)2 --------------> (4)2 (√2)2  -----------------> 16(2) = 32!!!

It looks like one of them may have misread the question.

D for diagonal and A for area and a for

The length of the side of the square.

We are given A=a^2 and by pythogorean theorem  we have D=(2)^(0.5)*a

So D^2=2*a^2=2*A=2*16=32

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