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The perimeter of a rectangle is 82 m and its area is $400 m^{2}$ . The breadth of the rectangle is

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25 m

20 m

16 m

9 m

answer is A, C.

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Detailed Solution

Given that the perimeter of the rectangle = 82m and area of the rectangle

= 400 m^{2}

.
Now, let's consider that the length and breadth of the rectangle are m and n respectively. We know that,
The perimeter of the rectangle

= 2 (length + breadth)

.
Then, perimeter of the rectangle= 82m

⟹ 2 (m + n) = 82

⟹ m + n = 41

⟹ m = 41 - n

…(1)
Now,
Area of the rectangle

= length \times breadth

.
Then,
Area of the rectangle=

400

⟹ m \times n = 400

⟹ n \times (41 - n) = 400

{Using (1)}

⟹ 41 n - n^{2} = 400

⟹ - n^{2} + 41 n = 400

⟹ n^{2} - 41 n + 400 = 0

⟹ n^{2} - 25 n - 16 n + 400 = 0

⟹ n (n - 25) - 16 (n - 25) = 0

⟹ (n - 16) (n - 25) = 0

⟹ n - 16 = 0 or n - 25 = 0

∴ n = 16 or n = 25

∴

The breadth of the rectangle is 16 or 25.
Hence, the correct options are 1 and 3.

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