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 4428 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 4427 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 4423 times ]
Area of rectangle = (base)(height)= (2)(5)
= 10
Answer: 10Cheers,
Brent
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