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The perimeter of the rectangular lawn is 54. It is reduced in size, so that length is $35 t h$ and breadth is $34 t h$ of the original dimensions. The perimeter of the reduced rectangle is $36 m$ .What were the original dimensions of the lawn?

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Length =16m, Breadth =11m

Length =25m, Breadth =22m

Length =13m, Breadth =10m

Length =15m, Breadth =12m

answer is D.

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Detailed Solution

Given that the perimeter of rectangle reduced to 36 from 54, when length reduced

35

and breadth reduced

34

.
Let the original length and breadth of the lawn are x and y, respectively, then,

2 (x + y) = 54 ⇒ x + y = 27 … (i) 2 35 x + 34 y = 36 ⇒ 4 x + 5 y = 120 … (i i)

From Eq. (i),

y = 27 − x

substituting in Eq. (ii),

4 x + 5 (27 − x) = 120 ⇒ − x = − 15 ⇒ x = 15

Substituting the value of x, in equation (i),

y = 27 − 15 = 12

Therefore, the rectangle sides are: Length =15m, Breadth =12m.
Hence, option (4) is correct.

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