Question

The length and breadth of a rectangle are in the ratio 5 : 4. If its perimeter is 72 cm, then find its length and breadth.

Answer 1

Answer:

Length is 20 cm and Breadth 16 cm.

Step-by-step explanation:

Given :

Ratio of the length to breadth = 5 : 4

Perimeter = 72 cm

To find :

The length and breadth of the rectangle

Solution :

Let the -

• Length be 5y
• Breadth be 4y

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

$\sf{\implies} \: 2(5y + 4y) = 72 \\ \\ \sf{\implies} \: 10y + 8y = 72 \\ \\ \sf{\implies} \: 18y = 72 \\ \\ \sf{\implies} \: y = \dfrac{72}{18} \\ \\ \sf{\implies} \: y =4$

$\rule{300}{1.5}$

★ Value of 5y

$\sf{\implies} \: 5 \times4 \\ \\ \sf{\implies} \: 20$

Length = 20 cm

$\rule{300}{1.5}$

★ Value of 4y

$\sf{\implies} \: 4 \times 4 \\ \\ \sf{\implies} \: 16$

Breadth = 16 cm

$\therefore$ Length is 20 cm and Breadth 16 cm.

Answer 2

$\huge\boxed{\bf{\red{SOLUTION:-}}}$

$\sf\underline{\blue{Given:-}}$

Sides of rectangle in ratio =5:4

and the perimeter of rectangle=72cm

Now

$\boxed{\sf{Perimeter\:of\: rectangle=2(l+b)}}$

$\sf\underline{\purple{Solution:-}}$

• Let the side of rectangle be x

• 5x and 4x

$\sf\implies 72=2(5x+4x)\\ \\ \sf\implies 72=2\times 9x\\ \\ \sf\implies 72=18x\\ \\ \sf\implies \cancel{\dfrac{72}{18}}=x\\ \\ \sf\implies 4=x$

• The value of x is 4

• Now the sides if rectangle

$\sf\:\:\bullet value\:of\:5x\\ \\ \sf {\blue{length=5\times 4=20cm}}\\ \\ \sf\:\:\bullet\:and\:value\:of\:4x\\ \\ \sf{\purple{Breadth=4\times 4=16cm}}$