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# In the figure above, Δ POQ and Δ AOB are both right-angled at point O.

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In the figure above, Δ POQ and Δ AOB are both right-angled at point O.  [#permalink]

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Updated on: 29 May 2017, 11:43
4
00:00

Difficulty:

65% (hard)

Question Stats:

66% (03:11) correct 34% (02:52) wrong based on 35 sessions

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In the figure above, Δ POQ and Δ AOB are both right-angled at point O. If BQ = OB and OA = AP, and the length of side AB is 5 units, what is the area of the shaded region?

(1) OA = OB + 1
(2) If a rectangle is drawn with sides of length 2QB and $$\frac{PA}{4}$$, the area of the rectangle will be 6 square units

Attachment:

oQ6sNCK.png [ 33.11 KiB | Viewed 823 times ]

Originally posted by niteshwaghray on 29 May 2017, 10:11.
Last edited by Bunuel on 29 May 2017, 11:43, edited 1 time in total.
Edited the question.
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Re: In the figure above, Δ POQ and Δ AOB are both right-angled at point O.  [#permalink]

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29 May 2017, 12:01
1

In the figure above, Δ POQ and Δ AOB are both right-angled at point O. If BQ = OB and OA = AP, and the length of side AB is 5 units, what is the area of the shaded region?

(1) OA = OB + 1

OA^2 + OB^2 = AB^2

(OB + 1)^2 + OB^2 = 5^2

We can find OB, then OA. We also know that BQ = OB and OA = AP. So, we know everything about the figure and will be able to answer the question. Sufficient.

(2) If a rectangle is drawn with sides of length 2QB and $$\frac{PA}{4}$$, the area of the rectangle will be 6 square units

2QB*PA/4 = 6;

Since BQ = OB and OA = AP, then 2OB*OA/4 = 6 --> OB*OA = 12 --> OA = 12/OB.

OA^2 + OB^2 = AB^2

(12/OB)^2 + OB^2 = 5^2

The same here: we can find OB, then OA. We also know that BQ = OB and OA = AP. So, we know everything about the figure and will be able to answer the question. Sufficient.

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Re: In the figure above, Δ POQ and Δ AOB are both right-angled at point O.  [#permalink]

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09 Aug 2019, 17:18
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Re: In the figure above, Δ POQ and Δ AOB are both right-angled at point O.   [#permalink] 09 Aug 2019, 17:18
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