Answer: ![90\ in^2](https://tex.z-dn.net/?f=90%5C%20in%5E2)
Step-by-step explanation:
The missing figure is attached.
Direct variation equations have the following form:
![y=kx](https://tex.z-dn.net/?f=y%3Dkx)
Where "k" is the Constant of variation.
Since the width of the rectangle varies directly as its length, you can write this equation:
![w=kl](https://tex.z-dn.net/?f=w%3Dkl)
Where "l" is the lenght in inches and "w" is the width in inches of the rectangle.
Observe in the figure that when
; then you can substitute them into the equation and solve for "k":
Therefore, the width is:
![w=(0.4)(15\ in)\\\\w=6\ in](https://tex.z-dn.net/?f=w%3D%280.4%29%2815%5C%20in%29%5C%5C%5C%5Cw%3D6%5C%20in)
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:
![A=(15\ in)(6\ in)\\\\A=90\ in^2](https://tex.z-dn.net/?f=A%3D%2815%5C%20in%29%286%5C%20in%29%5C%5C%5C%5CA%3D90%5C%20in%5E2)