Question

The breadth of a rectangular hall is three-fourth of its length. If the area of the floor is 768 sq. m, then the difference between the length and breadth of the hall is​

Answer 1

Step-by-step explanation:

Let the length of rectangular hall be x

We are given that The breadth of a rectangular hall is three-fourths of its length.

Breadth =\frac{3}{4}x

4

3

x

Area of hall =Length \times Breadth = x \times \frac{3}{4} x=\frac{3}{4}x^2Length×Breadth=x×

4

3

x=

4

3

x

2

The area of the floor is 768 sq m

\frac{3}{4}x^2 = 768

4

3

x

2

=768

x^2 = \frac{768 \times 4}{3}x

2

=

3

768×4

x=\sqrt{\frac{768 \times 4}{3} }x=

3

768×4

x=32

Length = 32 m

Breadth = \frac{3}{4}(32)=24 m

4

3

(32)=24m

Difference between length and breadth = 32 - 24 = 8 m

Hence the difference between the length and breadth of the hall is 8 m

Answer 2

Question:-

The breadth of a rectangular hall is three-fourth of its length. If the area of the floor is 768 sq. m, then what is the difference between the length and breadth of the hall?

Required Answer:-

Given:-

• Breadth of the rectangular hall is three-fourth of the length.
• Area of the floor is 768sq.m.

To Find:-

• Difference between the length and the breadth of the hall.

Solution:-

• Let the length of the rectangular hall be x

Therefore,

• Breadth of the rectangular hall = 3/4 × x = 3x/4

We know that:-

• Area of a rectangle = (Length × breadth) sq.units

According to the question:-

=> x × 3x/4 = 768

=> 3x^2/4 = 768

=> 3x^2 = 768 × 4

=> 3x^2 = 3072

=> x^2 = 3072/3

=> x^2 = 1024

=> √[x^2] = √1024

=> x = 32

Hence, the length of the hall = 32m

Now,

Breadth of the hall = 3/4 × x = 3/4 × 32 = 24m

And breadth of the hall = 24m

Finally,

Difference between the length and the breadth of the hall = (32-24)m = 8m

Hence, the difference between the length and the breadth of the rectangular hall is 8m