Question

18. A rectangle on a digital display board is made

so that its width varies directly as its length. The
current rectangle displayed is shown below. What
is the area of a rectangle that is 15 inches long?
(12.5 in.
5 in.

Answer 1

Answer:
`90\ in^2`

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)\\\\(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`