Question

The length of swimming pool in Virac Resort is 8 m longer than its width and the area is 105m^{2}[/tex]

Answer 1

It has given that, the length of swimming pool in Virac resort is 8m longer than its width and the area of is 105 m².

We have to find the length and width of swimming pool.

solution : let width of swimming pool is x then length of swimming pool is (x + 8)

now area of swimming pool = area of rectangle = length × width

⇒105 = (x + 8)x = x² + 8x

⇒x² + 8x - 105 = 0

⇒x² + 15x - 7x - 105 = 0

⇒x(x + 15) - 7(x + 15) = 0

⇒(x + 15)(x - 7) = 0

⇒x = 7, -15 but x can't be negative so, x = 7 m i.e., width = 7 m and length = 8 + 7 = 15m

therefore the length and width of swimming pool are 15m and 7 m respectively.

Answer 2

GivEn :-

• The Length of a swimming pool = 8m long than its width.

• Area of the pool = 105m2

To FinD :-

• The Length and the Width of the pool

SoluTioN :-

We Know that Area of a Rectangle = Length * Width. The pool is Rectangular In shape.

Area of pool = 105m2

• Let Width be x

• Let Length be (x + 8 )

★ Area = Lenghth * Width

$→ 105 = (x + 8)x \\ \\ → {x}^{2} + 8x - 105 = \\ \\ x(x + 8) - 7(x + 15) \\ \\→ (x - 7)(x + 15) \\ \\ → x = 7 \: or \: - 15 \\ \\ \bold{★The \: Length \: and \: Width \: will \: not \: be \: - ve}{} \\ \\ \bold{ \red{★Hence \: x = 7}{} }{}$

Therefore,

${ \bold{ \red{★x = 7 = width}{} }{} }{} \\ \ \\{ \bold{ \red{★(x + 8) = 15 = length}{} }{} }{}$