Answer:
The formula for calculating the width of the window is
[tex]w=\frac{-(-3)(+/-)\sqrt{-3^{2}-4(1)(2)}} {2(1)}[/tex]
Step-by-step explanation:
The question in English is
A rectangular window is l meters wide and h meters high, with a perimeter of 6 meters and an area of 2m². What is the formula for calculating the width of the window?
we know that
The perimeter of the window is equal to
[tex]P=2(l+w)[/tex]
we have
[tex]P=6\ m[/tex]
so
[tex]6=2(l+w)[/tex]
simplify
[tex]3=(l+w)[/tex]
isolate the variable l
[tex]l=3-w[/tex] ----> equation A
The area of the window is equal to
[tex]A=lw[/tex]
we have
[tex]A=2\ m^2[/tex]
so
[tex]2=lw[/tex] ----> equation B
substitute equation A in equation B
[tex]2=(3-w)w[/tex]
solve for w
[tex]2=3w-w^2[/tex]
[tex]w^2-3w+2=0[/tex]
The formula to solve a quadratic equation of the form
[tex]ax^{2} +bx+c=0[/tex]
is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]w^2-3w+2=0[/tex]
so
[tex]a=1\\b=-3\\c=2[/tex]
substitute in the formula
[tex]w=\frac{-(-3)(+/-)\sqrt{-3^{2}-4(1)(2)}} {2(1)}[/tex] ---> formula for calculating the width of the window
[tex]w=\frac{3(+/-)\sqrt{1}} {2}[/tex]
[tex]w=\frac{3(+/-)1} {2}[/tex]
[tex]w=\frac{3(+)1} {2}=2\ m[/tex]
[tex]w=\frac{3(-)1} {2}=1\ m[/tex]
