Question

the perimeter of a rectangular field is 82 metre and its area is 400 square metre find the length and breadth of the rectangle

Answer 1

Answer:

$82 = 2 \times x + y$

$x + y = 82 \div 2$

$x + y = 41$

Step-by-step explanation:

$x \times y = 400$

Answer 2

Answer:

Step-by-step explanation:

Solution :-

We know that 2(length + breadth) = perimeter

(Length + breadth) = 1/2 × 82 = 41 m.

Let the length of the field be x metres.

Then, its breadth = (41 - x) m.

Therefore,

Area of field = x(41 - x) m² = (41 - x²) m².

But, area = 400 m²

⇒ 41x - x² = 400

⇒ x² - 41x + 400 = 0

⇒ x² - 25x - 16x + 400 = 0

⇒ x(x - 25) - 16(x - 25) = 0

⇒ (x - 25) (x - 16) = 0

⇒ x - 25 = 0 or x - 16 = 0

⇒ x = 25, 16

When x = 25

Length = x = 25 m.

Breadth = 41 - x = 41 - 25 = 16 m.

When x = 16

Length = x = 16 m.

Breadth = 41 - x = 41 - 16 = 25 m.

Hence, the length and breadth of the rectangle is 25 m and 16 m or 16 m and 25 m.