Question

if breadth of a rectangle is one-third of it's length and it's area is 27 sq.cm. Find its perimeter​

Answer 1

$\overline{\underline{\boxed{\sf GIVEN \darr}}}$

If breadth of a rectangle is one-third of it's length and it's area is 27 cm². Find its perimeter.

$\overline{\underline{\boxed{\sf SOLUTION \darr}}}$

Let us assume :

The constant multiple be x

The perimeter is x

The breadth is 1/3 of the perimeter which means 1/3x

According to given information Area is 27 cm²

We know the formula for Area :

$\star \: \underline{ \boxed{\pink{ \frak{Area \: of \: the \: rectangle = Length × Breadth}}}}$

Putting the values we get

$\mapsto \frak{ \green{27 \: {cm}^{2} = x \times \frac{1}{3}x}}$

$\mapsto \frak{ \blue{27 \: {cm}^{2} = \frac{1}{3} {x}^{2} }}$

Now, by cross multiplying we get :

$\mapsto \frak{\purple{27 \: {cm}^{2} \times 3 = {x}^{2} }}$

$\mapsto \frak{ \red{ {x}^{2} = 81 \: {cm}^{2} }}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \star \: \underline{ \boxed{ \frak{ \orange{x = 9 \: cm}}}}$

_________________________________________

Now, the value of Length and Breadth is

Length = x

• Length = 9 cm

Breadth = 1/3x

Breadth = 1/3 × 9 cm

• Breadth = 3 cm

We know that formula for getting Perimeter is :

$\: \: \: \: \: \: \: \: \: \: \star \underline{ \boxed{\frak{ \blue{ {\sf P}erimeter = 2(Length + Breadth)}}}}$

• Perimeter = 2(9 cm + 3 cm)

• Perimeter = 2(12 cm)

• Perimeter = 24 cm

Henceforth, the perimeter of the rectangle is 24 cm

Answer 2

Answer:—

→ Perimeter of the rectangle is 24 cm.

Step by Step explanation:—

Given:—

If the breadth of a rectangle is 1/3 of its length and its area is 27 cm².

To find:—

• Perimeter of the rectangle.

Solution:—

Consider,

Length of the rectangle = x cm

★ The breadth of the rectangle is 1/3 of its length.

Then,

Breadth of the rectangle = x ×(1/3) = x/3 cm

★ Area of the rectangle is 27 cm².

According to the question :-

$\to\sf{x\times\dfrac{x}{3}=27}$

$\to\sf{\dfrac{x^2}{3}=27}$

$\to\sf{x^2=27\times\:3}$

$\to\sf{x^2=81}$

$\to\sf{x=\sqrt{81}}$

$\to\sf{x=9}$

★ Length of the rectangle = 9 cm.

★ Breadth of the rectangle = 9×(1/3) = 3 cm

Formula used :-

${\boxed{\sf{Perimeter\:of\: rectangle=2(Length+Breadth)}}}$

Perimeter of the rectangle,

→ {2(9+3) } cm

→ 2 × 12 cm

→ 24 cm.

Therefore,

The perimeter of the rectangle is 24 cm.