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If the diagonal of a square garden is 20 feet long, what is the perime

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Bunuel
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If the diagonal of a square garden is 20 feet long, what is the perime [#permalink] New post   05 Jul 2021, 02:45
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If the diagonal of a square garden is 20 feet long, what is the perimeter of the garden?

(A) 10√2 feet
(B) 20√2feet
(C) 40 feet
(D) 40√2 feet
(E) 80 feet
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D
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If the diagonal of a square garden is 20 feet long, what is the perime [#permalink] New post   06 Jul 2021, 21:35
Side of square = Diagonal/\sqrt{2}

Side = 20/\sqrt{2} = 10\sqrt{2}
Perimeter = 4 * Side = 40\sqrt{2}
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Re: If the diagonal of a square garden is 20 feet long, what is the perime [#permalink] New post   07 Jul 2021, 08:12
Bunuel wrote:
If the diagonal of a square garden is 20 feet long, what is the perimeter of the garden?

(A) 10√2 feet
(B) 20√2feet
(C) 40 feet
(D) 40√2 feet
(E) 80 feet

\(a\sqrt{2}=20\)

So, \(a = \frac{20}{\sqrt{2}}\)

Or,\(a = \frac{20\sqrt{2}}{\sqrt{2}*\sqrt{2}}\)

Or, \(a = 10\sqrt{2}\)

Thus perimeter will be \(4*10\sqrt{2}=40\sqrt{2}\), Answer will be (D)
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Re: If the diagonal of a square garden is 20 feet long, what is the perime [#permalink] New post   09 Jul 2021, 00:00
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Bunuel wrote:
If the diagonal of a square garden is 20 feet long, what is the perimeter of the garden?

(A) 10√2 feet
(B) 20√2feet
(C) 40 feet
(D) 40√2 feet
(E) 80 feet


Solution –

The formula for the diagonal of a square is \(√2 a \) where a = side of the square.
Now, \(√2 a = 20\)

\(a = \frac{20}{√2}\)

Perimeter = \(4a = 4(\frac{20}{√2})=40√2 \)

Answer D
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Re: If the diagonal of a square garden is 20 feet long, what is the perime [#permalink]
09 Jul 2021, 00:00
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