Question

18. A rectangle on a digital display board is made

Answer 1

Answer: $90\ in^2$

Step-by-step explanation:

The missing figure is attached.

Direct variation equations have the following form:

$y=kx$

Where "k" is the Constant of variation.

Since  the width  of the rectangle varies directly as its length, you can write this equation:

$w=kl$

Where "l" is the lenght in inches and "w" is the width in inches of the rectangle.

Observe in the figure that when $l=12.5\ in;\ w=5\ in$; then you can substitute them into the equation and solve for "k":

$5=k(12.5)\\\\\frac{5}{12.5}=k\\\\k=0.4$

Therefore, the width is:

$w=(0.4)(15\ in)\\\\w=6\ in$

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:

$A=(15\ in)(6\ in)\\\\A=90\ in^2$