Question

A rectangle rectangular room has an area of 216 square metre. If the perimeter of the room is 60 metre. What will be the length and breadth?​

Answer 1

Step-by-step explanation:

length=l

breadth=b

area of the rectangle =l×b

perimeter of the rectangle=2(l+b)

l×b=216

2(l+b)=60

l+b=30

l=30-b

(30-b)b=216

30b-b^2=216

b^2-30b+216

solve this equation u can get a answer

Answer 2

Answer:

$\bigstar{\bold{Length\:=18\:m,breadth=12\:m}}$

                 OR

$\bigstar{\bold{Length\:=12\:m,breadth=18\:m}}$

Step-by-step explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• Area of the room = 216 m²
• Perimeter of the room = 60 m

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• Length
• Breadth

$\Large{\underline{\underline{\bf{Solution:}}}}$

⇝ Here we have to find the length and breadth of the rectangle

⇝ The area of a rectangle is given by,

    Area of a rectangle = l × b

    where l = length

    b = breadth

⇝ Substitute the value for area

    216 = l × b

    216/l = b -----(1)

⇝ Now the perimeter of the rectangular room is given by,

    Perimeter of a rectangle = 2 (l + b)

⇝ Substitute the value of perimeter,

    60 = 2 (l + b)

⇝ Substitute the value of b from equation 1

   60/2 = l + 216/l

   30 = (l² + 216)/l

   l² - 30l + 216 = 0

⇝ Solving by splitting the middle term

    l² - 18l - 12l + 216 = 0

    l (l - 18) - 12 (l  - 18 ) = 0

    (l - 18) (l - 12) = 0

    l = 18 or l =12

⇝ If length of the room is 18 m,

    then breadth = 216/18 = 12 m

    $\boxed{\bold{Length\:=18\:m,breadth=12\:m}}$

⇝ If length of the room is 12 m,

    then breadth = 216/12 = 18 m

    $\boxed{\bold{Length\:=12\:m,breadth=18\:m}}$

$\Large{\underline{\underline{\bf{Notes:}}}}$

⇝ The area of a rectangle is given by,

    Area of rectangle = length × breadth

⇝ The perimeter of a rectangle is given by,

    Perimeter of rectangle = 2 (length + breadth)