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In the rectangular solid above, TU=3

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Joined: 07 Jun 2014
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GRE 1: Q167 V156
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In the rectangular solid above, TU=3 [#permalink] New post 01 Dec 2015, 18:40
Expert's post
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Question Stats:

86% (00:39) correct 13% (00:34) wrong based on 22 sessions
Attachment:
#GREpracticequestion In the rectangular solid above, TU=3, UV=4.jpg
#GREpracticequestion In the rectangular solid above, TU=3, UV=4.jpg [ 6.75 KiB | Viewed 765 times ]



In the rectangular solid above, TU=3, UV=4, and VR=2. What is the area of the shaded rectangular region?

[Reveal] Spoiler: OA
10


Practice Questions
Question: 12
Page: 150
Difficulty: easy

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GRE Prep Club Legend
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Joined: 07 Jun 2014
Posts: 4809
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 123

Kudos [?]: 1971 [0], given: 397

Re: In the rectangular solid above, TU=3 [#permalink] New post 01 Dec 2015, 18:44
Expert's post
Solution

Here we have in the rectangle RSTV the side RS = 2 and VT is the hypotenuse of the right triangle VTU where TU = 3 and UV = 4.

By Pythagoras theorem for right triangle we know that

VT = \(\sqrt{3^2 + 4^2}\) =5

So the Area of the shaded region = \(2 * 5\)= 10.
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Re: In the rectangular solid above, TU=3 [#permalink] New post 08 Jun 2019, 16:26
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sandy wrote:
Attachment:
The attachment #GREpracticequestion In the rectangular solid above, TU=3, UV=4.jpg is no longer available



In the rectangular solid above, TU=3, UV=4, and VR=2. What is the area of the shaded rectangular region?



Notice that that we have a right triangle in the diagram.
Attachment:
In the rectangular solid above, TU=3, UV=4, and VR=21.png
In the rectangular solid above, TU=3, UV=4, and VR=21.png [ 28.99 KiB | Viewed 286 times ]


You might recognize that 3 and 4 are part of the Pythagorean Triplet 3-4-5, in which case the missing side has length 5


Alternatively, we can apply the Pythagorean Theorem.
If we let x = the length of the hypotenuse of the triangle, we can write: 3² + 4² = x²
Simplify: 9 + 16 = x²
Simplify: 25 = x²
Solve: [b]x = 5[/b]
Attachment:
In the rectangular solid above, TU=3, UV=4, and VR=22.png
In the rectangular solid above, TU=3, UV=4, and VR=22.png [ 29.62 KiB | Viewed 287 times ]



At this point, we should see that the shaded rectangular region has dimensions 2 by 5
Attachment:
In the rectangular solid above, TU=3, UV=4, and VR=23.png
In the rectangular solid above, TU=3, UV=4, and VR=23.png [ 29.72 KiB | Viewed 286 times ]

Area of rectangle = (base)(height)
= (2)(5)
= 10

Answer: 10

Cheers,
Brent
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Re: In the rectangular solid above, TU=3   [#permalink] 08 Jun 2019, 16:26
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