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

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 $w = \frac{1}{4}l$

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

$A = wl = \dfrac{1}{4}l\cdot l = \dfrac{1}{4}l^2$

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

$9 = \dfrac{1}{4}l^2$

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:

$l = \sqrt{36} = 6$

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

$\dfrac{1}{4} \cdot 6 = \dfrac{6}{4} = \dfrac{3}{2} = 1.5$

Answer 2

Answer:

1.5

Step-by-step explanation: