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# The area of square ABCD is x 2 + 18 √ 3 x + 243 . What is the length

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Joined: 01 May 2016
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The area of square ABCD is x 2 + 18 √ 3 x + 243 . What is the length  [#permalink]

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11 Feb 2018, 09:40
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45% (medium)

Question Stats:

68% (02:08) correct 32% (02:00) wrong based on 43 sessions

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The area of square ABCD is x^ 2 + 18 √ 3 x + 243 . What is the length of the square's diagonal?

A) x+9√3

B) 4x+36√3

C) (x+9√3)^2

D)√2 (x+9√3)

E) (x+9√3)/√2

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Joined: 02 Sep 2009
Posts: 50039
The area of square ABCD is x 2 + 18 √ 3 x + 243 . What is the length  [#permalink]

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11 Feb 2018, 09:56
Tridhipal wrote:
The area of square ABCD is x^ 2 + 18 √ 3 x + 243 . What is the length of the square's diagonal?

A) x+9√3

B) 4x+36√3

C) (x+9√3)^2

D)√2 (x+9√3)

E) (x+9√3)/√2

The area of a square = $$\frac{diagonal^2}{2}$$.

$$x^2 + 18 \sqrt{3}x + 243 = (x +9\sqrt{3})^2=\frac{diagonal^2}{2}$$;

$$diagonal^2=2(x +9\sqrt{3})^2$$;

$$diagonal=\sqrt{2}(x +9\sqrt{3})$$.

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The area of square ABCD is x 2 + 18 √ 3 x + 243 . What is the length &nbs [#permalink] 11 Feb 2018, 09:56
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