Question

the length of the room is 3 meters greater than its breadth, if the area of the room is 180 square meters find the length and breadth of the room

Answer 1

Answer :

• Length of the rectangle = 15m
• Breadth of the rectangle = 12m

Given :

• Length of the room is 3m greater than it's breadth.
• Area of the room = 180m².

To Find :

• Length and breadth of the room.

Solution :

Let

• Breadth of the room = x
• Length of the room = x + 3

Here, the room is in the shape of a rectangle.

As we know that

• Area of a rectangle = l × b

Where

• l = length of the rectangle
• b = breadth of the rectangle

According to question :

➟ Area of the rectangle = 180

➟ x (x + 3) = 180

➟ x² + 3x = 180

➟ x² + 3x - 180 = 0

Now, it's in the form of quadratic equation

➟ x² + 15x - 12x - 180 = 0

Split the middle term

➟ x (x + 15) - 12 (x + 15) = 0

➟ (x - 12) (x + 15) = 0

➟ x = 12, -15

Therefore, x = 12 [ ignore negative value ]

Put the value of x

• Breadth of the rectangle = x = 12m
• Length of the rectangle = x + 3 = 12 + 3 = 15m

Hence,

• Dimensions of the rectangle are 15m and 12m respectively.

Answer 2

Question :

ㅤㅤㅤㅤㅤㅤ

the length of the room is 3 meters greater than its breadth, if the area of the room is 180 square meters find the length and breadth of the room

ㅤㅤㅤㅤㅤㅤ

Given :

• Area of room = 180m²
• Length of the room is 3m greater than its breadth.

To find :

• Length and breadth of the room.

Solution :

Let breadth of the room = x m

Let length = x + 3 ㅤㅤㅤㅤㅤㅤ(given)

ㅤㅤㅤㅤㅤㅤ

$\boxed {\tt Area \: of \: rectangle \: = \: length \times breadth }$

ㅤㅤㅤㅤㅤㅤ

$: \implies \tt { 180 = x \times (x + 3)}$

ㅤㅤㅤㅤㅤㅤ

$: \implies \tt {180 = x^2 + 3x }$

ㅤㅤㅤㅤㅤㅤ

$: \implies \tt { x^2 + 3x - 180 = 0}$

ㅤㅤㅤㅤㅤㅤ

$:\implies \tt {x^2 + 15x - 12x - 180 = 0}$

ㅤㅤㅤㅤㅤㅤ

$\small \mathfrak\green{\underline {By \: middle \: term \: splitting :}}$

ㅤㅤㅤㅤㅤㅤ

$:\implies \tt {x (x + 15) - 12 (x + 15) = 0}$

ㅤㅤㅤㅤㅤㅤ

$: \implies \tt { (x+ 15) (x-12) =0 }$

ㅤㅤㅤㅤㅤㅤ

$: \implies \tt { x = -15 , 12 }$

ㅤㅤㅤㅤㅤㅤ

ㅤㅤㅤㅤㅤㅤ

$\boxed {\tt Breadth\: of \: the \: room = x = 12 m}$

ㅤㅤㅤㅤㅤㅤ

$\boxed {\tt Length \: of \: the \: room = x + 3 = 12 + 3 = 15m}$