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

Question

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

Zarrolou · Answer

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

vinnik · Answer

What does this line " half as long again as it is broad " really mean ?

Vinni

vinnik · Answer

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

vinnik · Answer

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.

I know i am becoming furious about this question. I just want to clear my doubt.

Bunuel, looking forward to your reply.

Thanks & Regards
Vinni

Bunuel · Answer

This is a poor quality question, so I wouldn't worry about it at all.

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

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