Question

The perimeter of a school hall was 128 m. The length of the school hall was 38 m longer than the breadth. What was the area of the school hall?​

Answer 1

Answer:

perimeter =128m

perimeter =128m let breadth be x

perimeter =128m let breadth be xso 2x+2x+38=128

perimeter =128m let breadth be xso 2x+2x+38=1284x=90

perimeter =128m let breadth be xso 2x+2x+38=1284x=90x=22.5m

perimeter =128m let breadth be xso 2x+2x+38=1284x=90x=22.5mso breadth =45m

perimeter =128m let breadth be xso 2x+2x+38=1284x=90x=22.5mso breadth =45m 2length = 128- 45=83 m

perimeter =128m let breadth be xso 2x+2x+38=1284x=90x=22.5mso breadth =45m 2length = 128- 45=83 mlength =41.5 m

perimeter =128m let breadth be xso 2x+2x+38=1284x=90x=22.5mso breadth =45m 2length = 128- 45=83 mlength =41.5 mArea =l x b

perimeter =128m let breadth be xso 2x+2x+38=1284x=90x=22.5mso breadth =45m 2length = 128- 45=83 mlength =41.5 mArea =l x b =41.5 x 22.5

perimeter =128m let breadth be xso 2x+2x+38=1284x=90x=22.5mso breadth =45m 2length = 128- 45=83 mlength =41.5 mArea =l x b =41.5 x 22.5 A =933.75sqm

Answer 2

Given :-

Perimeter of a school hall = 128 m

The length of the school hall was 38 m longer than the breadth.

To Find :-

The area of the school hall.

Analysis :-

Consider the breadth as a variable and then the length would be 38 more than the length.

Substitute the values accordingly in the formula of perimeter of rectangle.

Once you get the length and breadth substitute them in the formula of area of rectangle.

Solution :-

We know that,

• l = Length
• b = Breadth
• a = Area
• p = Perimeter

Let the breadth be 'x'. Then the length would be x + 38.

By the formula,

$\underline{\boxed{\sf Perimeter \ of \ rectangle=2(Length +Breadth)}}$

Given that,

Perimeter (p) = 128 m

Substituting their values,

128 = 2(x+38 + x)

128 = 2(2x + 38)

128 = 4x + 76

4x = 128 - 76

4x = 52

x = 13

Breadth = 13 m

Length = x + 38

= 13 + 38 = 51 m

Therefore, the length and breadth are 51 m and 13 m respectively.

By the formula,

$\underline{\boxed{\sf Area \ of \ the \ rectangle=Length \times Breadth}}$

Given that,

Length (l) = 51 m

Breadth (b) = 13 m

Substituting their values,

Area = 51 × 13

Area = 663 m²

Therefore, the area of the school hall is 663 m².