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Which is greater h or w
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03 Sep 2025, 08:56
03 Sep 2025, 08:56
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Question Stats:
83% (01:33) correct
16% (01:29) wrong based on 6 sessions
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Quantity A |
Quantity B |
h |
w |
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Re: Which is greater h or w
[#permalink]
03 Sep 2025, 19:47
03 Sep 2025, 19:47
1
W is greater.
1) by extending h and w, we can deduce that the whole triangle is a right angle triangle so x=45°
2)both the smaller triangle also are right angle triangle.
3) extend the 2 and 3 segments until the whole hypotenuse by a and by b. We can clearly see that the small triangle also will be a right angle triangle; 90°;45°;45° and ratio of distance are a; a; asqrtroot2 thus a=b
Then tan 45°=1 = w/(3+a) = h/(2+a)
—-> w=[(3+a)/(2+a)]*h
a is positive that means 3+a> 2+a therefore (3+a)/(2+a) = 1+ [a/(2+a)]always >1
Overall, W>h
Posted from my mobile device
1) by extending h and w, we can deduce that the whole triangle is a right angle triangle so x=45°
2)both the smaller triangle also are right angle triangle.
3) extend the 2 and 3 segments until the whole hypotenuse by a and by b. We can clearly see that the small triangle also will be a right angle triangle; 90°;45°;45° and ratio of distance are a; a; asqrtroot2 thus a=b
Then tan 45°=1 = w/(3+a) = h/(2+a)
—-> w=[(3+a)/(2+a)]*h
a is positive that means 3+a> 2+a therefore (3+a)/(2+a) = 1+ [a/(2+a)]always >1
Overall, W>h
Posted from my mobile device
gmatclubot
Re: Which is greater h or w [#permalink]
03 Sep 2025, 19:47
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