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The area is (2x + 15) square centimeters.
The ratio of the shaded region to the unshaded region is 3 : 2.
Write an algebraic expression for the area of the shaded region in terms of x.

Respuesta :

Poltergeist

Answer:

[tex]Area\:shaded=\frac{3}{5} (2x+15)[/tex]

Step-by-step explanation:

Let [tex]s[/tex] be the shaded area and [tex]u[/tex] be the unshaded area, then we know that

(1).  [tex]\frac{s}{u}=\frac{3}{2}[/tex]

and

(2).   [tex]s+u=(2x+15)[/tex]

We solve for [tex]u[/tex] in the first equation and get:

[tex]u=\frac{2}{3}s[/tex]

and put this into the second equation and get:

[tex]s+\frac{2}{3}s=(2x+15)[/tex]

[tex]s(1+\frac{2}{3} )=(2x+15)[/tex]

[tex]s(\frac{5}{3} )=(2x+15)[/tex]

[tex]\boxed{s=\frac{3}{5} (2x+15)}[/tex]

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