Question

a field is twice as long as it is wide.it has a perimeter of 540m.what is its area

Answer 1

Long= Length

Wide= Breadth

Step-by-step explanation:

so let the length be 2x and breadth be x

so perimeter of rectangle = 2(l+b)

so,

$2 \times (2x + x) = 540 \\ 2 \times (3x) = 540 \\ 6x = 540 \\ x = \frac{540}{6} \\ x = 90$

so

$bredth = 90 \: m \\ length = 90 \times 2 = 180m$

Answer 2

Given :

Perimetre of the rectangle : 540 m

The longest side is 2 times as the shortest side.

To find :

The area of the rectangle.

Solution :

As we know that the longest side is the length and the shortest side is the breadth. So, first we should find the lengths be breadth of the rectangle.

Let the length be 2y metres.

Let the breadth be y metres.

Breadth of the rectangle :

$\sf \dashrightarrow {Perimetre}_{(Rectangle)} = 2 \: (Length + Breadth)$

$\sf \dashrightarrow 540 = 2 \: (2y + y)$

$\sf \dashrightarrow 540 = 2 \: (3y)$

$\sf \dashrightarrow 2 \: (3y) = 540$

$\sf \dashrightarrow 3y = \dfrac{540}{2}$

$\sf \dashrightarrow 3y = 270$

$\sf \dashrightarrow y = \dfrac{270}{3}$

$\sf \dashrightarrow y = 90$

Now, let's find the find the length of the rectangle.

Length of the rectangle :

$\sf \dashrightarrow 2y = 2(90)$

$\sf \dashrightarrow 180 \: metres$

Now, we can find the area of the rectangle.

Area of the rectangle :

$\sf \dashrightarrow {Area}_{(Rectangle)} = Length \times Breadth$

$\sf \dashrightarrow 180 \times 90$

$\sf \dashrightarrow 16200 \: metres^2$

Hence, the area of the rectangle is 16200 metres².