# 9. The width of a rectangular hall is 1/2 of its length. If the area of the hall is 450 sq.m, what is thedifference between its length and breadth?n​

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• Width of a rectangular hall is 1/2 of its length

• Area of the hall is 450 sq. m

• Difference between its length and breadth

• Let the length be "x"

• Let the width be "y"

➠ Length × Breadth ------- (1)

Width of a rectangular hall is 1/2 of its length

So,

--- (2)

• Length = x

• Width = y =

Putting these values in (1)

➜ x ×

➜ x ×

➜ x² = 450 × 2

➜ x² = 900

x = -30

➨ x = 30 ------- (3)

Length can't be negative , hence x = 30

• Hence length of rectangular hall is 30 m

➨ y = 15

• Hence width of rectangular hall is 15 m

Now we need to find the difference between its length and breadth

➠ x - y

➜ 30 - 15

➨ 15

∴ The difference between its length and breadth is 15 m

3

Given:

The width of a rectangular hall is 1/2 of its length.

Area of the hall = 450 m²

To Find:

Difference between the hall's length and breadth

Solution:

• What is the area of a rectangle?

The Area of a rectangle is given by:

• As per the given question,

Let the length of the rectangular hall be x m

Then the width of the hall will be m

• Now we put these variables into the formula for area:

(x). () = 450

⇒ = 450

⇒ x² = 900

⇒  x = √900 = 30

Therefore, length of the hall = 30 m

And the width of the hall = = 15 m

Hence, difference between length and width

= 30 -15

= 15 m

## Therefore, the difference between its length and breadth is 15 m.

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