Question

ᵗʰᵉ ˡᵉⁿᵍᵗʰ ᵒᶠ ᵃ ʳᵉᶜᵗᵃⁿᵍˡᵉ ˡᵒᵗ ⁱˢ 6 ˡᵉˢˢ ᵗʰᵃⁿ ᵗʰʳⁱᶜᵉ ⁱᵗˢ ʷⁱᵈᵗʰ, ⁱᶠ ᵗʰᵉ ᵃʳᵉᵃ ⁱˢ 45 ˢᵠᵘᵃʳᵉ ᶜᵐ, ʷʰᵃᵗ ⁱˢ ᵗʰᵉ ˡᵉⁿᵍᵗʰ ᵃⁿᵈ ᵗʰᵉ ʷⁱᵈᵗʰ ᵒᶠ ᵗʰᵉ ʳᵉᶜᵗᵃⁿᵍˡᵉ?

Answer 1

$\;\;\underline{\textbf{\textsf{ Given :-}}}$

• The length of a rectangular lot is 6 less than thrice it's width.

• Area of the rectangular lot is = 45 cm²

$\;\;\underline{\textbf{\textsf{ To Find :-}}}$

• Length and width of the given rectangle

$\;\;\underline{\textbf{\textsf{ Solution :-}}}$

Let the width of the rectangular lot be x units.

Given that,

The length of a rectangular lot is 6 less than thrice it's width.

Then, the length will be = (3x -6) units

$\underline{\:\textsf{We know that :}}$

$\star\;{\boxed{\sf{\purple{Area_{\;(Rectangle)} = Length × Breadth)}}}}$

$\underline{\:\textsf{ Now, put the given values :}}$

$\dashrightarrow \sf 45 = (3x-6) × x$

$\dashrightarrow \sf 45 = 3x² - 6x$

$\dashrightarrow \sf 0= 3x² - 6x-45$

$\dashrightarrow \sf 0= 3x(x - 5) + 9(x - 5)$

$\dashrightarrow \sf 0= (3x + 9)(x - 5)$

$\dashrightarrow {\boxed{\frak{\purple{x= 5}}}}\;$

( As width can't be negative)

ㅤ$\;\;\underline{\textbf{\textsf{ Hence-}}}$

$\underline{\textsf{ Length and width of the rectangle are \textbf{ 9 and 5 units respectively }}}.$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Answer 2

Answer:

width = 5cm

length = 9cm

Step-by-step explanation:

to find : length and width

Given :

area = 45cm²

length = 3(width) - 6

Let :

width = x

length = 3x - 6

Solution :

area of rectangle = length × width

area = (3x-6) × (x)

=> 45 = 3x² -6x

dividing by 3 on each side

=> 45/3 = (-6x/3) + 3x²/3

=> 15 = x² - 2x

=> x² - 2x - 15 = 0

splitting middle term

=> x² - (5-3)x - 15 = 0

=> x² - 5x + 3x - 15 = 0

=> x(x-5) + 3(x- 5) = 0

=> (x-5)(x+3) = 0

either (x-5) = 0 .........or........ (x+3) = 0

either x = (5) ...........or........ x = (-3)

as side cannot be negative

therefore

x = 5

=> width = x = 5cm

=> length = 3x-6 = 3(5)-6 = 15-6

=> length = 9cm