Respuesta :
Given :-
- The length of a rectangle is 6 more than the width
- Area of rectangle = 720 feet²
[tex] \\ [/tex]
To find:-
- Length
- Width
[tex] \\ [/tex]
Let :-
- Width of rectangle = x
- Length of rectangle = 6 + x
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Solution:-
So to find length and width of rectangle, we have to find value of x.
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We know:-
[tex] \bigstar \boxed{ \rm Area~of~rectangle=Length\times{}Width}[/tex]
By using this formula we can find value of x.
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So:-
[tex] \\ [/tex]
[tex] \dashrightarrow\sf Area~of~rectangle=Length\times{}Width \\ [/tex]
[tex] \\ [/tex]
[tex] \dashrightarrow\sf 720=(x + 6)(x)[/tex]
[tex] \\ [/tex]
[tex] \dashrightarrow\sf 720=x(x) +x( 6)[/tex]
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[tex] \dashrightarrow\sf 720= {x}^{2} +x( 6)[/tex]
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[tex] \dashrightarrow\sf 720= {x}^{2} +6x[/tex]
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[tex] \dashrightarrow\sf0 = {x}^{2} +6x - 720[/tex]
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[tex] \dashrightarrow\sf {x}^{2} +6x - 720 = 0[/tex]
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[tex] \dashrightarrow\sf {x}^{2} +30x - 24x - 720 = 0[/tex]
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[tex] \dashrightarrow\sf ({x}^{2} +30x )- 24x - 720 = 0[/tex]
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[tex] \dashrightarrow\sf x({x}+30 )- 24x - 720 = 0[/tex]
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[tex] \dashrightarrow\sf x({x}+30 ) + (- 24x - 720) = 0 \\ [/tex]
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[tex] \dashrightarrow\sf x({x}+30 ) - 24(x+ 30) = 0 \\ [/tex]
[tex] \\ [/tex]
[tex] \dashrightarrow\sf (x - 24)({x}+30 )= 0 \\ [/tex]
[tex] \\ [/tex]
We got two solutions:-
first solution
- x - 24 = 0
- x = 24
Second solution :-
- x + 30 = 0
- x = -30
Length can't be taken negative so 24 is the value of x.
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Value of width:-
- Width of rectangle = x
- Width = 24 feet
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Value of Length:-
- Length of rectangle = x + 6
- Length = 24 + 6
- Length = 30 feet