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In the figure above, ABCD is a rectangle, and each of AP and CQ is per : Multiple-choice Questions — Select One Answer Choice

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Re: In the figure above, ABCD is a rectangle, and each of AP and CQ is per [#permalink]
tanzy1 wrote:
consider AB=5 so Triangle APB= 3-4-5 right angled triangle hence, AP=3 PB=PQ+QB=4 so PQ=QB=DP=2
Now in triangle APD, AP=3,DP=2 So AD= sqrt13 SO, AB:AD= 5:SQRT13 = 1.4 so option A


Hi tanzy1,
Can you please explain the highlighted part?
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In the figure above, ABCD is a rectangle, and each of AP and CQ is per [#permalink]
3
Consider only triangle DAB.
AD^2 + AB^2 = (3x)^2, where x=DP = PQ = QB
AD^2 + AB^2 = 9x^2
Any combination of the sum for AB^2 and AD^2 must be a factor of 9x^2. Let's plug in x=1

(A) \(\sqrt{2}\) to 1 ---> 2+1=3, a factor of 9

(B) \(\sqrt{3}\) to 1 ---> 3+1=4, not a factor of 9

(C) \(\sqrt{3}\) to \(\sqrt{2}\) ---> 3+2=5, not a factor of 9

(D) 2 to 1 ---> 4+1=5, not a factor of 9

(E) 2 to \(\sqrt{3}\) ---> 4+3=7, not a factor of 9

Hence, answer is A

GeminiHeat wrote:
Image
In the figure above, ABCD is a rectangle, and each of AP and CQ is perpendicular to BD. If DP = PQ = QB, what is the ratio of AB to AD?


(A) \(\sqrt{2}\) to 1

(B) \(\sqrt{3}\) to 1

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

(D) 2 to 1

(E) 2 to \(\sqrt{3}\)
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Re: In the figure above, ABCD is a rectangle, and each of AP and CQ is per [#permalink]
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Re: In the figure above, ABCD is a rectangle, and each of AP and CQ is per [#permalink]
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