Question

the perimeter of rectangle is 36 cm and its length is twice the breadth calculate the area

Answer 1

breadth=6cm

and length=12cm

Answer 2

Given :

• Perimeter of rectangle = 36 cm
• Length of rectangle = 2 × Breadth of rectangle

To Find :

• Area of rectangle = ?

Solution :

Let breadth of rectangle be "x"

Therefore, According to Statement :

$\sf : \implies length = 2 \times x$

$\sf : \implies length = 2x$

Now, we have :

• Perimeter = 36 m

We have formula of perimeter of rectangle :

$\large \underline{\boxed{\bf{Perimeter_{(rectangle)} = 2(Length + Breadth)}}}$

By filling values :

$\sf : \implies 36 \: m = 2(2x + x)$

$\sf : \implies 36 \: m = 2 \times 3x$

$\sf : \implies 36 \: m = 6x$

$\sf : \implies x = \cancel{\dfrac{36}{6}} \: m$

$\sf : \implies x = 6 \: m$

$\large \underline{\boxed{\bf{x = 6 \: m}}}$

So, we have value of "x"

Now,

• length = 2x = 2 × 6 m = 12 m
• breadth = x = 6 m

So, to find area, we have a formula :

$\large \underline{\boxed{\bf{Area_{(rectangle)} = Length \times Breadth}}}$

$\sf : \implies Area_{(rectangle)} = 12 \: m \times 6 \: m$

$\sf : \implies Area_{(rectangle)} = 72 \: m^{2}$

$\large \underline{\boxed{\bf{Area_{(rectangle)} = 72 \: m^{2}}}}$

Hence, area of rectangle is 72 m²