Question

lenght of a rectangular plot is twice its breadth,if the perimeter is 30cm then what is the area?​

Answer 1

let length be`L`. and breadth be `B`

L=2B

perimetre(P)=2(L+B)

30=2(L+B)

30=2(2B+B)

30=4B+2B

30=6B

5=B

L=2B

L=2*5

L=10

area=L*B

area=10*5

Area=50

Answer 2

Given :-

Length of a rectangular plot = 2 × Breadth

Perimeter of the rectangle = 30 cm

To Find :-

The area of the rectangular plot.

Analysis :-

At first, we have to find the length and breadth.

Consider the breadth as a variable then the length would be two times the variable.

Make an equation accordingly by substituting them in the formula of perimeter of a rectangle.

Get the value of the variable and substitute it in the length as well.

In order to find the area, substitute the values in it's respective formula.

Solution :-

We know that,

• l = Length
• b = Breadth
• a = Area

Let the breadth of the rectangle be 'x'. Then the length would be '2x'.

By the formula,

$\underline{\boxed{\sf Perimeter \ of \ rectangle=2(Length \times Breadth)}}$

Given that,

Perimeter = 30 cm

Length (l) = 2x

Breadth (b) = x

Substituting their values,

30 = 2(2x + x)

30 = 2(3x)

30 = 6x

x = 30/6

x = 5

Therefore,

Breadth (b) = 5 cm

Length (l) = 2x

= 2 × 5 = 10 cm

Therefore, the length and breadth are 10 cm and 5 cm respectively.

By the formula,

$\underline{\boxed{\sf Area \ of \ rectangle=Length \times Breadth}}$

Given that,

Length (l) = 10 cm

Breadth (b) = 5 cm

Substituting their values,

Area = 10 × 5

Area = 50 cm²

Therefore, the area of the rectangle is 50 cm².