Answer: [tex]90\ in^2[/tex]
Step-by-step explanation:
The missing figure is attached.
Direct variation equations have the following form:
[tex]y=kx[/tex]
Where "k" is the Constant of variation.
Since the width of the rectangle varies directly as its length, you can write this equation:
[tex]w=kl[/tex]
Where "l" is the lenght in inches and "w" is the width in inches of the rectangle.
Observe in the figure that when [tex]l=12.5\ in;\ w=5\ in[/tex]; then you can substitute them into the equation and solve for "k":
[tex]5=k(12.5)\\\\\frac{5}{12.5}=k\\\\k=0.4[/tex]
Therefore, the width is:
[tex]w=(0.4)(15\ in)\\\\w=6\ in[/tex]
Since the area of the rectangle can be calculated multiplying its lenght by its width, you get that the area of the rectangle that is 15 inches long is:
[tex]A=(15\ in)(6\ in)\\\\A=90\ in^2[/tex]
