Question

The perimeter of a rectangle is 82 metre and its area is 400 square metres the breadth of rectangle is

Answer 1

Given:

• Perimeter of rectangle = 82 m

• Area of rectangle = 400 m²

To find out:

Find the breadth of given rectangle?

Formula used:

• Perimeter of rectangle = 2 ( l + b )

• Area of rectangle = l × b

Solution:

Let breadth be b.

According to the question,

Perimeter = 2 ( l + b )

⇒2 ( l + b ) = 82

⇒l + b = 41

⇒ l = 41- b ...........( 1 )

Now,

Area of rectangle = l × b

⇒l × b = 400

⇒b × ( 41 - b ) = 400 [ from ( 1 ) ]

⇒ 41b - b² = 400

⇒ 41b - b² - 400 = 0

⇒ b² - 41b + 400 = 0

⇒ b² - 25b - 16b + 400 = 0

⇒ b ( b - 25 ) - 16 ( b - 25 ) = 0

⇒ ( b - 25 ) ( b - 16 ) = 0

⇒ b = 25 or b = 16

Answer 2

$\huge\mathfrak\green{Answer:}$

Given:

It is given that the perimeter of a rectangle is 82m and its area is 400m^2.

To Find:

We need to find the breadth of rectangle.

Solution:

Let the length of rectangle be l and breadth be b.

We know that the permanent of rectangle is 2(l + b).

As it is given that perimeter is 82m so we have,

2(l + b) = 82m

=> (l + b) = 82/2

=> (l + b) = 41

or l = 41 - b __________(1)

But, it is also given that the area of rectangle is 400m^2.

We know that area of rectangle is l × b, So we have,

l × b = 400m^2

=> (41 - b) × b = 400m^2 [From equation 1]

=> 41b - b^2 = 400m^2

=> - b^2 + 41b - 400 = 0

Or, b^2 - 41b + 400 = 0

Now by splitting the middle term we have,

b^2 - (25b + 16b) + 400 = 0

=> b^2 - 25b - 16b + 400 = 0

=> b(b - 25) - 16(b - 25) = 0

= (b - 25) (b - 16)

Therefore, b is either 25 or 16.