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In square ABCD above, E is the midpoint of side BC. If DE = 8√5, what [#permalink]
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05 Oct 2017, 01:36
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Re: In square ABCD above, E is the midpoint of side BC. If DE = 8√5, what [#permalink]
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05 Oct 2017, 02:54
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In square ABCD above, E is the midpoint of side BC. If DE = 8√5, what is the length of a side of the square?
Let side of Square = 2a = DC = BC => BE = a
Given DE = 8√5
In triangle DEC => \(DE^2 = DC^2 + CE^2\) => \((8√5)^2 = (2a)^2 +a^2\) => \(64*5 = 5a^2\) => \(a^2 = 64\) => a=8
Answer: D



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Re: In square ABCD above, E is the midpoint of side BC. If DE = 8√5, what [#permalink]
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05 Oct 2017, 04:35
In square ABCD above, E is the midpoint of side BC. If DE = 8√5, what is the length of a side of the square?
Let side of Square = 2a = DC = BC => BE = a
Given DE = 8√5
In triangle DEC => DE2=DC2+CE2DE2=DC2+CE2 => (8√5)2=(2a)2+a2(8√5)2=(2a)2+a2 => 64∗5=5a264∗5=5a2 => a2=64a2=64 => a=8
Answer: D



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In square ABCD above, E is the midpoint of side BC. If DE = 8√5, what [#permalink]
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05 Oct 2017, 05:03
Nikkb wrote: In square ABCD above, E is the midpoint of side BC. If DE = 8√5, what is the length of a side of the square?
Let side of Square = 2a = DC = BC => BE = a
Given DE = 8√5
In triangle DEC => \(DE^2 = DC^2 + CE^2\) => \((8√5)^2 = (2a)^2 +a^2\) => \(64*5 = 5a^2\) => \(a^2 = 64\) => a=8
Answer: D Yes, but BE is a half of a side, so we should double it to 16, right? Isn't correct answer A?



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Re: In square ABCD above, E is the midpoint of side BC. If DE = 8√5, what [#permalink]
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05 Oct 2017, 12:03
Bunuel wrote: In square ABCD above, E is the midpoint of side BC. If DE = 8√5, what is the length of a side of the square? (A) 16 (B) 6√5 (C) 4√5 (D) 8 (E) 2√6 Attachment: 20171004_1125.png let the side of square be x \(x^2 + (x^2)/4 = (8\sqrt{5})^2\) x^2 = 16^2 x=16 A
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Re: In square ABCD above, E is the midpoint of side BC. If DE = 8√5, what [#permalink]
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05 Oct 2017, 22:36
Let DC=2x Therefore, CE=x
So, in Triangle CDE, Using Pythagoras: DE=x√5 So, x√5=8√5 , x=8 Hence, each side of square=2x=16.
Ans A
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In square ABCD above, E is the midpoint of side BC. If DE = 8√5, what [#permalink]
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06 Oct 2017, 14:46
Bunuel wrote: In square ABCD above, E is the midpoint of side BC. If DE = 8√5, what is the length of a side of the square? (A) 16 (B) 6√5 (C) 4√5 (D) 8 (E) 2√6 Attachment: 20171004_1125.png Careful if you use \(x\) and \(2x\) to solve. I found out the hard way. The length of a side in that case is not \(x\). It is 2\(x\) As the midpoint of a side, E marks onehalf the length of a side. So CE = half a side. The square's bottom side, CD, and CE = legs of a right triangle CDE whose hypotenuse is length 8√5. Let CE = x and CD = 2x \(x^2 + (2x)^2 = (8√5)^2\) \(5x^2 = (64)(5)\) \(x^2 = 64\) \(x = 8\) Side CD (or any side) is 2x. Side of square = (2 * 8) = 16 Answer A
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Re: In square ABCD above, E is the midpoint of side BC. If DE = 8√5, what [#permalink]
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06 Oct 2017, 15:53
Nikkb wrote: In square ABCD above, E is the midpoint of side BC. If DE = 8√5, what is the length of a side of the square?
Let side of Square = 2a = DC = BC => BE = a
Given DE = 8√5
In triangle DEC => \(DE^2 = DC^2 + CE^2\) => \((8√5)^2 = (2a)^2 +a^2\) => \(64*5 = 5a^2\) => \(a^2 = 64\) => a=8
Answer: D Same solution, but a is 1/2 the side of the square. Side = 2a = 16.



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Re: In square ABCD above, E is the midpoint of side BC. If DE = 8√5, what [#permalink]
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09 Oct 2017, 16:44
Bunuel wrote: In square ABCD above, E is the midpoint of side BC. If DE = 8√5, what is the length of a side of the square? (A) 16 (B) 6√5 (C) 4√5 (D) 8 (E) 2√6 Attachment: 20171004_1125.png We can let DC = n and EC = (1/2)n. Using the Pythagorean theorem, we can determine n: n^2 + (n/2)^2 = (8√5)^2 n^2 + (n^2/4) = 320 4n^2 + n^2 = 320 x 4 5n^2 = 320 x 4 n^2 = 64 x 4 n = 8 x 2 = 16 Answer: A
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Re: In square ABCD above, E is the midpoint of side BC. If DE = 8√5, what [#permalink]
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10 Oct 2017, 07:58
Let each side of the square be x. CD=x, CE=x/2 (Since E is midpoint of the side) In right angled triangle CDE, by Pythagoras theorem \(x^2+(x/2)^2\)=(8\(\sqrt{5})\)^2=64*5 \(\frac{5x^2}{4}\) = 64*5 x^2 = 64 * 4 x=8*2 = 16 Answer A.
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Re: In square ABCD above, E is the midpoint of side BC. If DE = 8√5, what [#permalink]
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11 Oct 2017, 11:38
Nikkb wrote: In square ABCD above, E is the midpoint of side BC. If DE = 8√5, what is the length of a side of the square?
Let side of Square = 2a = DC = BC => BE = a
Given DE = 8√5
In triangle DEC => \(DE^2 = DC^2 + CE^2\) => \((8√5)^2 = (2a)^2 +a^2\) => \(64*5 = 5a^2\) => \(a^2 = 64\) => a=8
Answer: D You got that right. a=16 but the question is asking for side of the square. Since side of the square will be 2a, the answer will be 16 (A)




Re: In square ABCD above, E is the midpoint of side BC. If DE = 8√5, what
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