sandy wrote:

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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.

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In the rectangular solid above, TU=3, UV=4, and VR=21.png [ 28.99 KiB | Viewed 2899 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]

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In the rectangular solid above, TU=3, UV=4, and VR=22.png [ 29.62 KiB | Viewed 2899 times ]
At this point, we should see that the shaded rectangular region has dimensions 2 by 5

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In the rectangular solid above, TU=3, UV=4, and VR=23.png [ 29.72 KiB | Viewed 2899 times ]
Area of rectangle = (base)(height)= (2)(5)

= 10

Answer: 10Cheers,

Brent

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