Question

the length of the rectanglel lot is 6 less than thrice its width if the area is 45 square cm. what is the length and width of the rectangle​

Answer 1

Answer:-

Let the breadth of the rectangle be x units.

Given:

Length of the rectangle is 6 less than thrice the breadth.

⟶ Length = (3x - 6) units

Also,

Area of the rectangle = 45 unit²

We know that,

Area of a rectangle = length * breadth

⟶ 45 = (3x - 6) * (x)

⟶ 45 = 3x² - 6x

⟶ 0 = 3x² - 6x - 45

⟶ 0 = 3x² - 15x + 9x - 45

⟶ 0 = 3x(x - 5) + 9(x - 5)

⟶ 0 = (3x + 9)(x - 5)

★ 3x + 9 = 0

⟶ 3x = - 9

⟶ x = - 9/3

⟶ x = - 3

★ x - 5 = 0

⟶ x = 5

Breadth cannot be negative. so - 3 is neglected.

Therefore,

• Length of the rectangle = 3x - 6 = 3(5) - 6 = 9 units
• Breadth of the rectangle = x = 5 units.

Answer 2

Given : The length of the rectangle lot is 6 less than thrice its width if the area is 45 square cm.

　

To find : What is the length and width of the rectangle?

　

Using formula :

★ Area = Length × Breadth.

　

Calculations :

• Let length be "BL - 6".
• Let breadth be "B".

　

→ 45 = (3B - 6) × B

→ 45 = 3B² - 6B

→ 3B² - 6B - 45 = 0

→ 3B² - 15B + 9B - 45 = 0

→ 3B (B - 5) + 9(B - 5) = 0

→ 3B + 9 = 0, B - 5 = 0

→ 3B = -9/3, B = 5

　

The value of Length or Breadth can't be negative so let's take the Positive value.

　

→ L = 3(5) - 6

→ L = 15 - 6

→ L = 9 units

　

→ B = 5 units

　

Therefore, this is the required answer.