Question

The area of a rectangular room is 165 sq. m. If its length is 4 m more than its breadth, what is thelength and breadth of the hall?​ ​

Answer 1

Step-by-step explanation:

Area =340m2

Breadth =17m

Length=BreadthArea

=17340

=20m

Perimeter =2(l+b)

=2(20+17)

=2(37)

=74m.

Answer 2

Given :

• The area of a rectangular room is 165m².

• The length of the rectangular room is 4m more than its breadth.

To find :

• The length and breadth of the hall.

Solution :

If we assume that :

➠Breadth of the rectangular room is x metre.

Than,

➠Length will be (x + 4) metres.

Hence,

We know that,

$\bold \dag{ \underline{ \boxed{ \bf{\gray {Area \: of \: the \: rectangle ={ l \times b}}}}}} \bold \dag$

Where,

➠ l(length) = x metre.

➠ b(breadth) = (x + 4) metre.

➠ Area of the rectangular room : 165m²

Procedure :

Substituting the given values as follows :

$\bf \implies \: area \: of \: the \: rectangular \: room = \{(x) \times (x + 4) \}$

$\bf \implies \: {165m}^{2} = {x}^{2} + 4 x$

$\bf \implies \: 0 = {x}^{2} + 4x - {165m}^{}$

$\bf \implies 0 = {x}^{2} + 15x - 4x - {165m}^{}$

$\bf \implies 0 = x(x - 15) + 4(x - 15)$

$\bf \implies 0 = (x - 15)(x + 4)$

$\bf \implies x = - 4$

$or,$

$\bf x = 15m$

After solving this problem we get :

➠x = -4

or,

➠x = 15

Here, we know that negative ( - ) sign can't be taken as a breadth of the rectangular room.

Hence,

Required answer :

Breadth of the rectangular room will be :

➠Breadth x = 15 metres.

And,

➠ Length will be :

➠ (x + 4)

➠ (15 + 4)

➠ 19 metres.

Note :

• Negative ( - ) signs can't be taken as any measurement or units for measuring.