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Q.

The perimeter of a rectangular plot is 60m and its area is 200 sq.m. The dimensions of the plot are


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a

20m × 18m

b

20m × 10m 

c

20m × 15m

d

22m × 10m

answer is D.

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Detailed Solution

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Given that perimeter of the rectangular plot =60m and area =200sq.m.
Let’s consider that the length and breadth of the rectangle are l and b respectively.  We know that,
The perimeter of the rectangle=2(length+breadth)
Then,
⟹2l+b=60
⟹l+b=30
⟹b=30-l         ….(1)
And
Area of the rectangle=length×breadth
Then,
⟹l×b=200
⟹l×30-l=200         {Using (1)}
⟹30l-l2=200
⟹-l2+30l=200
⟹l2-30l+200=0
⟹l2-20l-10l+200=0
⟹ll-20-10l-20=0
⟹l-10l-20=0
⟹l-10=0 or l-20=0
⟹l=10 or l=20
For l=10,
⟹b=30-l=30-10=20 For l=20,
⟹b=30-l=30-20=10 ∴The dimensions of the plot are 20m × 10m.
Hence, option (4) is correct.
 
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