Question

The length of a rectangular hall is 3m more than its breadth. If the area of the hall is 130cm square ,find its perimeter and it's answer is 46cm​

Answer 1

Answer:

Given :-

• The length of a rectangular hall is 3 cm more than its breadth.
• The area of the hall is 130 cm².

To Find :-

• What is the perimeter of a rectangular hall.

Solution :-

Let,

$\mapsto \bf Breadth_{(Rectangular\: Hall)} =\: x\: cm$

$\mapsto \bf Length_{(Rectangular\: Hall)} =\: (x + 3)\: cm$

Given :

• The area of the hall = 130 cm²

According to the question by using the formula we get,

$\small \implies \boxed{\bold{Area_{(Rectangle)} =\: Length \times Breadth}}$

$\implies \sf 130 =\: (x + 3) \times x$

$\implies \sf 130 =\: (x + 3)x$

$\implies \sf 130 =\: x^2 + 3x$

$\implies \sf x^2 + 3x - 130 =\: 0$

$\implies \sf x^2 + (13 - 10)x - 130 =\: 0$

$\implies \sf x^2 + 13x - 10x - 130 =\: 0$

$\implies \sf x(x + 13) - 10(x + 13) =\: 0$

$\implies \sf (x + 13)(x - 10) =\: 0$

$\implies \sf x + 13 =\: 0$

$\implies \bf x =\: - 13\: \: \: \bigg\lgroup \bf Dimensions\: can't\: be\: negetive \bigg\rgroup$

Or,

$\implies \sf x - 10 =\: 0$

$\implies \bf x =\: 10$

Hence, the value of x is 10 .

So, the required length and breadth of a rectangular hall is :

$\dag$ Length of Rectangular Hall :

$\footnotesize \longrightarrow \bf Length_{(Rectangular\: Hall)} =\: (x + 3)\: cm =\: (10 + 3)\: cm =\: 13\: cm$

$\dag$ Breadth of Rectangular Hall :

$\footnotesize \longrightarrow \bf Breadth_{(Rectangular\: Hall)} =\: x\: cm =\: 10\: cm$

Now, we have to find the perimeter of a rectangular hall :

Given :

• Length = 13 cm
• Breadth = 10 cm

According to the question by using the formula we get,

$\small \dashrightarrow \sf\boxed{\bold{Perimeter_{(Rectangle)} =\: 2(Length + Breadth)}}$

So,

$\dashrightarrow \sf Perimeter_{(Rectangular\: Hall)} =\: 2(13 + 10)$

$\dashrightarrow \sf Perimeter_{(Rectangular\: Hall)} =\: 2(23)$

$\dashrightarrow \sf\bold{Perimeter_{(Rectangular\: Hall)} =\: 46\: cm}$

$\therefore$ The perimeter of a rectangular hall is 46 m .

Answer 2

Question :-

• The length of a rectangular hall is 3m more than its breadth. If the area of the hall is 130cm square ,find its perimeter and it's answer is 46cm

Concept :-

• In this question, the area of a rectangular hall is 130 cm² , the length is x + 3 and the breadth is x. We will apply the area of a rectangle and find out the length and breadth of the rectangular hall. Then, atlast we will find the perimeter of the rectangular hall.

Solution :-

★ Area of a rectangle = l × b ★

Where,

l = length

b = breath.

★ Area = ( x + 3) x

= 130 cm² = x² + 3x

= x² + 3x - 130 = 0

= x² + ( 13 - 10)x - 130 = 0

= x² + 13x - 10x - 130 = 0

= x(x + 13) - 10(x + 13) = 0

= (x + 13) + ( x - 10) = 0

= (x + 13) = 0 OR (x - 10) = 0

Since, value of x cannot be negative. So the value of x is 10 .

★ Length and breadth of the rectangular hall :-

★ length = x + 3 = 10 + 3 = 13 cm.

★ Breadth = x = 3 cm.

Perimeter of the rectangular hall :-

★ Perimeter of a rectangle = 2( l + b ) ★

Where,

l = length

b = Breadth

★ Perimeter = 2( 13 + 3 )

Perimeter = 2( 16)

Perimeter = 32 cm.

Therefore,the perimeter of the rectangular hall is 32 cm.

Joyful learning!!!⛅