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

$\huge{ \underline{\underline{ \bold { \blue{ \sf{question}}}}}}$

• 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?

$\huge{ \underline{\underline{ \bold { \blue{ \sf{formula}}}}}}$

• Area of rectangle= length × breadth
• perimeter of rectangle = 2(l+b)

$\huge{ \underline{\underline{ \bold { \blue{ \sf{solution}}}}}}$

ATQ

Perimeter of rectangle = 2(length + breadth)

= 60=2(length +breadth)

30 = length + breadth

30 - length = breadth -----------(1)

Area of rectangle= length × breadth

216 = length × breadth

216 = length ×( 30- length ) { from eq 1}

216 = 30 length - length²

Let the length be x

216 = 30x-x²

x²-30x+216 = 0

So a=1 ,b=-30 and c=216

X= -b+√b²-4ac/2a

x= 30+√ 30²-4(1)(216)/2

x= 30+√900-864

x=30±6

x=30-6

x= 24 or x= 30+6 = 36

So length can be 24 or 36

Answer 2

Answer:

Length = 12m and Breadth = 18m

OR

Length = 18m and Breadth = 12m

Step-by-step explanation:

We are given,

A rectangle with area 216 m² and perimeter 60 m.

Let the length of the rectangle be 'l' and breadth be 'b'

We know that,

Perimeter of a Rectangle = 2(l + b)

Thus,

60 = 2(l + b)

l + b = 60/2

l + b = 30

∴ l = 30 - b ----- 1

Now, we also know that,

Area of a rectangle = l × b

216 = l × b

From eq.1 we get,

216 = (30 - b)b

30b - b² = 216

b² - 30b + 216 = 0

xb² + yb + z = 0

where x = 1, y = -30, z = 216

Using Factorization method,

Sum = y = -30

Product = x × z = 216

Thus, the factors are -12 and -18

So,

b² - 12b - 18b + 216 = 0

b(b - 12) - 18(b - 12) = 0

(b - 18)(b - 12) = 0

Now, one of the factors must give 0 to make the whole equation equal to 0.

Hence,

b = 18 or b = 12

Now,

From eq.1 we get,

Case 1

l = 30 - 18

l = 12 m

Case 2

l = 30 - 12

l = 18 m

Thus,

Length = 12m and Breadth = 18m

OR

Length = 18m and Breadth = 12m

Hope it helped and you understood it........All the best