Question

A rectangle’s width is one-fourth of its length. Its area is 9 square units. The equation l(1/4l) = 9 can be used to find l, the length of the rectangle.

Answer 1

1.5

Explanation:

Answer 2

I see no actual question, but I'm assuming that you want to find the dimensions of the rectangle.

In general, the area of a rectangle with width
`w` and length
`l` is

`A = wl`

In this case, we know that the width is one-fourth of its length, which means
`w = (1)/(4)l`

If we plug this expression for w in the formula for the area, we get

`A = wl = (1)/(4)l\cdot l = (1)/(4)l^2`

We also know that the area is 9 squared units, so we have

`9 = (1)/(4)l^2`

If we multiply both sides by 4, we get

`l^2 = 36`

Consider the square root of both sides (we only accept the positive solution, since a negative length would make no sense:

`l = √(36) = 6`

So, the length is 6, and the width is one-fourth of 6, i.e.

`(1)/(4) \cdot 6 = (6)/(4) = (3)/(2) = 1.5`