Question

a rectangular field has an 24 square meters and a perimeter of 20 metres. find the breadth of the field​

Answer 1

Answer:

Breadth = 4 m or 6 m

Step-by-step explanation:

Given:

• Area = 24 m²
• Perimeter = 20 m

To find:

Breadth of the field = ?

Solution:

Let:

• Length be x
• Breadth be y

We know that in a rectangle;

   Perimeter = 2 (Length + Breadth)

⇒ 20 = 2 (x + y)

⇒ 20 ÷ 2 = (x + y)

⇒ x + y = 10           ------ [Equation ➀]

Also,

   Area = Length × Breadth

⇒ 24 = x × y

⇒ xy = 24

⇒ x = 24/y          ------ [Equation ➁]

Substitute the value of x from Equation 2 in Equation 1.

x + y = 10

$\implies \sf{\dfrac{24}{y}+y=10}$

On taking LCM,

$\implies \sf{\dfrac{24+y^{2}}{y}=10}$

$\implies \sf{24+y^{2}=10y}$

$\implies \sf{y^{2}-10y+24=0}$

$\implies \sf{y^{2}-6y-4y+24=0}$

$\implies \sf{y(y-6)-4(y-6)=0}$

$\implies \sf{(y-4)(y-6)=0}$

Hence,

The value of y = 4 or 6

∴ The Breadth of the field = 4 m or 6 m