Question

at the perimetre of a rectangle is 240m is 5:3. find the area of the rectangle anghe gatio of the length and he breadth​

Answer 1

Answer:

3375 m²

Step-by-step explanation:

As per the provided information in the given question, we have:

• The perimeter of rectangule is 240 m.
• The ratio between the length and breadth is 5 : 3.

We've been asked to calculate the area of the rectangle.

Let us suppose the length of the rectangle as 5x and the breadth of the rectangle as 3x.

$\odot$ Perimeter of rectangle is twice the sum of it's length and breadth.

$\twoheadrightarrow\quad\sf{P=2(l+b)}$

According to our assumption and given in the question,

$\twoheadrightarrow\quad\sf{240=2(5x+3x)}$

Performing addition inside the bracket. $\\\twoheadrightarrow\quad\sf{240=2(8x)}$

Performing multiplication.

$\twoheadrightarrow\quad\sf{240=16x}$

Transposing 16 from RHS to LHS. It's arithmetic operator will get change. $\\\twoheadrightarrow\quad\sf{\dfrac{240}{16}=x}$

Performing division in order to calculate the value of x.

$\twoheadrightarrow\quad\sf{x=15}$

We've calculated the value of x that is 15. As we have a assumed that the length and breadth of the rectangle as 5x and 3x. Thus,

$\twoheadrightarrow\quad\sf{Length=5x}$

Substitute value of x in order to perform multiplication.

$\twoheadrightarrow\quad\sf{Length=5\times 15}$

Performing multiplication in order to calculate the length of the rectangle.

$\twoheadrightarrow\quad\sf{Length=75}$

Now, let us calculate the breadth of the rectangle.

$\twoheadrightarrow\quad\sf{Breadth=3x}$

Substitue value of x in order to perform multiplication.

$\twoheadrightarrow\quad\sf{Breadth=3\times 15}$

Performing multiplication in order to calculate the breadth of the rectangle.

$\twoheadrightarrow\quad\sf{Breadth=45}$

Now, we have to calculate the area of the rectangle. As, we know that area of rectangle is the product of length and breadth. So,

$\twoheadrightarrow\quad\sf{Area=l\times b}$

Substitute the value of l and b.

$\twoheadrightarrow\quad\sf{Area=75\times 45}$

Now, performing multiplication in order to calculate the area of the rectangle.

$\twoheadrightarrow\quad\underline{\boxed{\pmb{\frak{Area=3375\; {m}^{2}}}}}$

❝ Therefore, the area of the rectangle is 3375 m². ❞