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