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In the figure, the diagonal BD of square ABCD is 3.

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In the figure, the diagonal BD of square ABCD is 3. [#permalink] New post 31 Jan 2019, 16:37
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In the figure, diagonal BD of square ABCD is 3. What is the perimeter of the square?

A) 4.5

B) 12

C) \(3 \sqrt{2}\)

D) \(6 \sqrt{2}\)

E) \(12 \sqrt{2}\)
[Reveal] Spoiler: OA

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Re: In the figure, the diagonal BD of square ABCD is 3. [#permalink] New post 01 Feb 2019, 08:28
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Solution,

Given,

ABCD is a square. So, all the sides are equal. i.e. AB = BC = CD = DA

Diagonal BD divides the square into two 45-45-90 right triangles.

By the application of Pythagoras theorem,

BD ^ 2 = BC ^ 2 + CD ^ 2

By the calculation, we found,

BD = CD = 3/√2

i.e. AB = BC = CD = DA = 3/√2

Now, Perimeter of a square = 4 * length
= 4 * 3/ √2
= 12 / √2
= 2 * 2 * 3 / √2
= √2 * √ 2 * 2 * 3/ √2
= 6 √2

Thus, the answer is D.
Re: In the figure, the diagonal BD of square ABCD is 3.   [#permalink] 01 Feb 2019, 08:28
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In the figure, the diagonal BD of square ABCD is 3.

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