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The area of a 6m wide road outside a garden in all its four is 564 sq meters. If the length of the garden is 20m, what is its breadth?
A) 15 m
B) 20 m
C) 25 m
D) 30 m

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Last updated date: 20th Jun 2024
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Answer
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Hint: An area is the size of a two-dimensional surface. The area of a rectangle is the space contained within a set of lines. To find out the area of a rectangle border, we need to subtract the area of the inner rectangle from the area of the outer rectangle.

Complete step-by-step answer:
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This gives details of a road around a garden – the path is 6m wide.
Let breadth of garden be x meters.
Length of garden=20 m
We can work out the dimensions of the outer section because we know the path around the edge is 6m wide.
Now the new length of a garden with road = 20 + 6 + 6 = 32 m
Now the new breadth of a garden with road = x + 6 + 6 = (x + 12) m
To find out the area of a rectangle border, we need to subtract the area of the inner rectangle from the area of the outer rectangle.
Given, the area of the road = 564 sq meters
Now, area of road= Area of the outer rectangle – area of the inner rectangle
$
   \Rightarrow 32(x + 12) - 20x = 564 \\
   \Rightarrow 32x + 384 - 20x = 564 \\
   \Rightarrow 12x = 564 - 384 = 180 \\
   \Rightarrow x = 15 \\
 $
So, Breadth of ground=15m
So, option (A) is the correct answer.

Note: Before solving the question make sure all the units of area, length and breadth etc are the same. If the units are different, convert them to the same unit and then solve the question.