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In the figure above, the shaded region is a square with area equal to
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22 Mar 2021, 10:14
22 Mar 2021, 10:14
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In the figure above, the shaded region is a square with area equal to 256. If AB = 8, then what is the length of diagonal AC?
Show: :: OA
24
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Re: In the figure above, the shaded region is a square with area equal to
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22 Mar 2021, 19:20
22 Mar 2021, 19:20
3
Shaded region is square with area of 256, so side will be 16
We have length AB = 8 , width = 16 = height
Diagonal AC = \(\sqrt{8^2+16^2+16^2}\) = 24
Answer 24
We have length AB = 8 , width = 16 = height
Diagonal AC = \(\sqrt{8^2+16^2+16^2}\) = 24
Answer 24
Re: In the figure above, the shaded region is a square with area equal to
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24 Mar 2021, 02:43
24 Mar 2021, 02:43
1
Assuming the vertex just below point A to be D, the basic idea to calculate the diagonal of a cuboid is first calculating the diagonal from D to C using Pythagoras theorem and then calculating the diagonal AC using Pythagoras theorem on the triangle ADC.
Diagonal DC =\(\sqrt{16^2 + 8^2}\)=\(\sqrt{320}\)
Diagonal AC=\(\sqrt{DC^2 + AD^2}\)=\(\sqrt{256+320}\)=24
Hence the length of diagonal AC=24
Diagonal DC =\(\sqrt{16^2 + 8^2}\)=\(\sqrt{320}\)
Diagonal AC=\(\sqrt{DC^2 + AD^2}\)=\(\sqrt{256+320}\)=24
Hence the length of diagonal AC=24
