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# If a square has a perimeter of x, then, in terms of x what is the leng

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If a square has a perimeter of x, then, in terms of x what is the leng  [#permalink]

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23 Aug 2018, 03:36
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If a square has a perimeter of x, then, in terms of x what is the length of the diagonal of the square?

A. $$4x\sqrt{2}$$

B. $$\frac{x\sqrt{2}}{2}$$

C. x^2/16

D. x/2

E. $$\frac{x\sqrt{2}}{4}$$

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Re: If a square has a perimeter of x, then, in terms of x what is the leng  [#permalink]

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23 Aug 2018, 03:43
Bunuel wrote:
If a square has a perimeter of x, then, in terms of x what is the length of the diagonal of the square?

A. $$4x\sqrt{2}$$

B. $$\frac{x\sqrt{2}}{2}$$

C. x^2/16

D. x/2

E. $$\frac{x\sqrt{2}}{4}$$

Perimeter=4*length of side=x
Or, length of side=x/4
Diagonal of square=$$\sqrt{2}$$* length of side=$$\sqrt{2}*\frac{x}{4}$$

Ans. (E)
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Re: If a square has a perimeter of x, then, in terms of x what is the leng  [#permalink]

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23 Aug 2018, 07:50
Bunuel wrote:
If a square has a perimeter of x, then, in terms of x what is the length of the diagonal of the square?

A. $$4x\sqrt{2}$$

B. $$\frac{x\sqrt{2}}{2}$$

C. x^2/16

D. x/2

E. $$\frac{x\sqrt{2}}{4}$$

Sides of the square = $$\frac{x}{4}$$

So, Diagonal of the square = $$\frac{x√2}{4}$$, Answer must be (E)
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Re: If a square has a perimeter of x, then, in terms of x what is the leng  [#permalink]

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26 Aug 2018, 19:16
Bunuel wrote:
If a square has a perimeter of x, then, in terms of x what is the length of the diagonal of the square?

A. $$4x\sqrt{2}$$

B. $$\frac{x\sqrt{2}}{2}$$

C. x^2/16

D. x/2

E. $$\frac{x\sqrt{2}}{4}$$

We can let n = side and create the perimeter equation:

4n = x

n = x/4
Recall that the diagonal of a square is the hypotenuse of a 45-45-90 triangle. Thus, we have:

Hypotenuse = Diagonal = side * √2 = x/4 * √2 = x√2/4

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Re: If a square has a perimeter of x, then, in terms of x what is the leng  [#permalink]

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26 Aug 2018, 19:33
Perimeter of square= x

Side of square must be= $$\frac{x}{4}$$

Diagonal of square= $$\sqrt{2}$$ * side of square= $$\frac{x}{4}\sqrt{2}$$

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Re: If a square has a perimeter of x, then, in terms of x what is the leng   [#permalink] 26 Aug 2018, 19:33
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