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# A rectangular plot is half as long again as it is broad

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Manager
Joined: 14 Dec 2011
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A rectangular plot is half as long again as it is broad [#permalink]  24 Apr 2013, 09:50
00:00

Difficulty:

65% (hard)

Question Stats:

22% (01:00) correct 78% (00:38) wrong based on 9 sessions
A rectangular plot is half as long again as it is broad and its area is 2/3 hectares. Then its length is:

(a) 100 m
(b) 33.33 m
(c) 66.66 m
(d) (100 \sqrt{3})/3 m
(e). 88.88 m

Thanks & Regards
Vinni
[Reveal] Spoiler: OA
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Re: A rectangular plot is half as long again as it is broad [#permalink]  24 Apr 2013, 10:06
vinnik wrote:
A rectangular plot is half as long again as it is broad and its area is 2/3 hectares. Then its length is:

(a) 100 m
(b) 33.33 m
(c) 66.66 m
(d) (100 \sqrt{3})/3 m
(e). 88.88 m

Thanks & Regards
Vinni

1 hectares = 100*100 squared meters

$$B*H=100000*\frac{2}{3}$$ and $$H=\frac{1}{2}B$$ so $$\frac{B*B}{2}=10000*\frac{2}{3}$$ $$B^2=10000*2*\frac{2}{3}$$

$$B^2=\frac{10000*4}{3}, B=\sqrt{\frac{10000*4}{3}}$$

$$B=\frac{100*2}{\sqrt{3}}$$ and $$H=\frac{100}{\sqrt{3}}$$

IMO D
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Manager
Joined: 14 Dec 2011
Posts: 66
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Kudos [?]: 17 [0], given: 66

Re: A rectangular plot is half as long again as it is broad [#permalink]  24 Apr 2013, 10:40
What does this line "half as long again as it is broad" really mean ?

Vinni
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Joined: 14 Dec 2011
Posts: 66
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Kudos [?]: 17 [0], given: 66

Re: A rectangular plot is half as long again as it is broad [#permalink]  24 Apr 2013, 11:13
Thanks Zarrolou.

In this question, answer is 100 i.e (A). And i can get this answer when i take one of the sides, suppose y = x + $$\frac{1}{2}x$$ =$$\frac{3x}{2}$$ then only i can get 100 as answer. In your above explanation you have taken $$H=\frac{1}{2}B$$
which gives D as the answer. This is where i am getting confused.

Can anyone please clarify on this.

Vinni
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Re: A rectangular plot is half as long again as it is broad [#permalink]  24 Apr 2013, 12:15
Hi Bunuel ,

I just came across the following question of your's
a-rectangular-garden-is-to-be-twice-as-long-as-it-is-wide-136877.html?fl=similar

I can see that the wording of my question matches the wording of the above question except i can see there is "again" mentioned in the sentence.

Thanks & Regards
Vinni
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Re: A rectangular plot is half as long again as it is broad [#permalink]  25 Apr 2013, 02:32
Expert's post
vinnik wrote:
Hi Bunuel ,

I just came across the following question of your's
a-rectangular-garden-is-to-be-twice-as-long-as-it-is-wide-136877.html?fl=similar

I can see that the wording of my question matches the wording of the above question except i can see there is "again" mentioned in the sentence.

Thanks & Regards
Vinni

This is a poor quality question, so I wouldn't worry about it at all.
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Re: A rectangular plot is half as long again as it is broad   [#permalink] 25 Apr 2013, 02:32
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