Question

The perimeter of a rectangular frame is 28 cm. if the length and breadth of the frame are in the ratio 2: 5 , find the area of the frame .
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Answer 1

Given:

• The perimeter of a rectangle frame = 28 cm
• The length and breadth of the rectangle are in ratio 2:5

To be found:

The area of the rectangle

So,

Let us first find the length and breadth of the rectangle frame with the help of the given ratio.

Let,

Length of the rectangle frame = 2x cm

And, breadth of the rectangle frame = 5x cm

The formula for finding the perimeter of the rectangle

= 2(l + b) units      

[∵ In which 'l' is the 'length' and 'b' is the 'breadth' of the rectangle]

So,

⇒ 2(l + b) = 28 ÷ 2

⇒ l + b = 14

⇒ 2x + 5x = 14

⇒ 7x = 14

⇒ x = 14÷ 7

⇒ x = 2

Value of x = 2

Now,

Length of the rectangle = 2x = 2 × 2 = 4cm

Breadth of the rectangle = 5x = 5 × 2 = 10 cm

Now

Area of the rectangle frame

= lb unit²

= 4 × 10 cm²

= 40 cm²

Hence,

The area of the rectangle frame is 40 cm²

Verification:

$\frac{4}{10} = \frac{2}{5}$

[dividing 2 to numerator and denominator]

And, 2(l+b)

= 2(4+10)

= 2(14)

= 28

Answer 2

Let length be 2x and breadth be 5x

Perimeter given = 28cm

So,

by putting the formula of perimeter

=> 28 = 2(2x+5x)

=> 28 = 2(7x)

=> 28 = 14x

=>28/14 = x

=> 2 = x

l = 2*2 = 4

and b = 5*2 = 10

area = length*breadth

= 4*10 = 40 cm sq.