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A rectangular garden is surrounded by a path of uniform width of 2 m. What is the breadth of the rectangular garden? I. If the length of the garden is reduced by 2 m, it will become a square garden. II. If the length of the garden is reduced by 2 m, the area of the path will become 1/4 times of its original area. (External boundary of the path remains constant.)

A rectangular garden is surrounded by a path of uniform width of 2 m. What is the breadth of the rectangular garden? I. If the length of the garden is reduced by 2 m, it will become a square garden. II. If the length of the garden is reduced by 2 m, the area of the path will become 1/4 times of its original area. (External boundary of the path remains constant.) Correct Answer <span style="color: rgb(37, 37, 37); ">If both the data given in both the statements are required;</span>

Let the original length be (l + 2) and breadth be b

Considering statement I:

⇒ (l + 2) - 2 = b

⇒ l = b

⇒ Area of the garden = l2

Considering statement II:

Length is reduced by 2 m

New length = l

Breadth = b

Total area includes the path

⇒ (l + 4) × (b + 4)

Area of path = (l + 4) × (b + 4) - lb = 1/4(lb)

By combining both the statements, we get : the length and breadth.

∴ It can be solved by using both the statements.

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