Question

A rectangular room is 9 feet longer than it is wide. The area of the room is 360 square feet. How many feet long is the room?

Answer 1

Given:

• A rectangular room is 9 feet longer than it is wide.

• Area of the room is 360 square feet.

To find out:

Find the length of room ?

Formula used :

Area of rectangle = length × breadth

Solution:

Let the breadth be x .

Then, Length,l = x + 9

According to the question,

Area of rectangle = length × breadth

★ Putting the values of length and breadth, we get:

⇒ 360 = ( x + 9 ) x

⇒ 360 = x² + 9x

⇒ x² + 9x - 360 = 0

⇒ x² + 24x - 15x - 360 = 0

⇒ x( x + 24) - 15(x + 24) = 0

⇒ ( x + 24 ) = 0 or ( x - 15 ) = 0

⇒ x = - 24 or x = 15 [ Negative number is ignored ]

Now,

Length,l = x + 9 = 15 + 9 = 24 feet

Thus,the length of room is 24 feet .

Answer 2

GIVEN:

• A rectangular room is 9 feet longer than it is wide.
• The area of the room is 360 square feet.

TO FIND:

• What is the length of the room ?

SOLUTION:

Let the length of the room be 'l' m and breadth be 'b' m

➪ A rectangular room is 9 feet longer than it is wide.

According to question:-

$\bf{\dashrightarrow l = b + 9....1) }$

We know that the formula for finding the area of the rectangular room is:-

$\large\bf{\star \: Area = Length \times Breadth \: \star}$

According to question:-

$\rm{\dashrightarrow 360 = (b+9) \times b }$

$\rm{\dashrightarrow 360 = b^2 + 9b }$

$\rm{\dashrightarrow b^2 + 9b - 360 = 0 }$

$\rm{\dashrightarrow b^2 +(24-15)b - 360 = 0 }$

$\rm{\dashrightarrow b^2 + 24b -15b -360 = 0 }$

$\rm{\dashrightarrow b(b + 24) -15(b + 24) = 0}$

$\rm{\dashrightarrow (b+24) (b-15) = 0}$

$\bf{\dashrightarrow b = -24 \: feet \: }$(Length can't be in negative)

$\bf{\dashrightarrow b = 15 \: feet }$

Put the value of 'b' in equation 1)

$\rm{\dashrightarrow l = 15 + 9 }$

$\bf{\dashrightarrow \star \: l = 24 \: feet \: \star }$

❝ Hence, the length of the rectangular room is 24 feet ❞

______________________