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In the rectangular solid shown

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In the rectangular solid shown [#permalink] New post 27 Dec 2016, 03:04
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Question Stats:

90% (00:36) correct 9% (03:36) wrong based on 11 sessions
Image

In the rectangular solid shown, TU=3, UV=4, and VR=2

Quantity A
Quantity B
The area of the shaded rectangular region
9


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: In the rectangular solid shown [#permalink] New post 29 Dec 2016, 12:39
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Expert's post
Carcass wrote:
Image

In the rectangular solid shown, TU=3, UV=4, and VR=2

Quantity A
Quantity B
The area of the shaded rectangular region
9



Notice that we have have a right triangle hiding in the diagram.
Image

So, we can apply the Pythagorean Theorem to find the length of the missing side.
If we let x = the length of side VT, we can write: 3² + 4² = x²
Evaluate to get 9 + 16 = x²
Add: 25 = x²
So, x = 5

We get:
Image

At this point, we can see that the shaded rectangle has dimensions 5 by 2
So, the area = (5)(2) = 10

We have:
Quantity A: 10
Quantity B: 9

Answer: A
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Re: In the rectangular solid shown   [#permalink] 29 Dec 2016, 12:39
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In the rectangular solid shown

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