Question

The perimeter of the floor of a rectangular hall is 46 m. Its length is 15 m. Find its area.​

Answer 1

Answer:

Given :-

• The perimeter of the floor of a rectangular hall is 46 m.
• It's length is 15 m.

To Find :-

• What is the area of a rectangular hall.

Formula Used :-

$\clubsuit$ Perimeter of Rectangle Formula :

$\footnotesize \bigstar \: \: \sf\boxed{\bold{\pink{Perimeter_{(Rectangle)} =\: 2(Length + Breadth)}}}\: \: \: \bigstar$

$\clubsuit$ Area of Rectangle Formula :

$\footnotesize \bigstar \: \: \sf\boxed{\bold{\pink{Area_{(Rectangle)} =\: Length \times Breadth}}}\: \: \: \bigstar$

Solution :-

First, we have to find the breadth of a rectangular hall :

Let,

$\mapsto \bf Breadth_{(Rectangle)} =\: b\: m$

Given :

• Perimeter = 46 m
• Length = 15 m

According to the question by using the formula we get,

$\footnotesize \implies \bf Perimeter_{(Rectangle)} =\: 2(Length + Breadth)$

$\implies \sf 46 =\: 2(15 + b)$

$\implies \sf 46 =\: 30 + 2b$

$\implies \sf 46 - 30 =\: 2b$

$\implies \sf 16 =\: 2b$

$\implies \sf \dfrac{\cancel{16}}{\cancel{2}} =\: b$

$\implies \sf \dfrac{8}{1} =\: b$

$\implies \sf 8 =\: b$

$\implies \sf\bold{\purple{b =\: 8\: m}}$

Hence, the breadth of a rectangular hall is 8 m .

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

Given :

• Length = 15 m
• Breadth = 8 m

According to the question by using the formula we get,

$\small \dashrightarrow \bf Area_{(Rectangular\: Hall)} =\: Length \times Breadth$

$\dashrightarrow \sf Area_{(Rectangular\: Hall)} =\: 15\: m \times 8\: m$

$\dashrightarrow \sf\bold{\red{Area_{(Rectangular\: Hall)} =\: 120\: m^2}}$

$\therefore$ The area of a rectangular hall is 120 m² .

Answer 2

Answer:

Hence the area of the floor of a rectangular hall (A) is $120\;m^{2} .$

Step-by-step explanation:

As per the data provided in the given question.

The given data is as follows,

The perimeter of the floor of a rectangular hall (P) is 46 m.

Length of the floor of a rectangular hall (l) is 15 cm.

We have to find the value of area of the floor of a rectangular hall (A).

At first, we will find the value of width (w).

Perimeter is given so here we will use the formula of perimeter of rectangle.

$P=2(l+w)$

Above formula we will write as bellow,

$w=\frac{P}{2}-l$

Now we will substitute the given values in above formula.

$w=\frac{46}{2}-15$

We will divide 46 by 2 we get

[tex]w=23-15\\ w=8\;m[/tex]

Now we will find the area of the floor of a rectangular hall (A).

Here we will be using the formula of area of rectangle.

$A=l\times w$

Now we will substitute the given values in above formula.

We get,

$A=15\times 8$

We will multiply 8 into 5 get 40 and 1 into 8.

Further, we get

$A=120\;m^{2}$

Hence the area of the floor of a rectangular hall (A) is $120\;m^{2} .$