Respuesta :
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 [tex]w[/tex] and length[tex]l[/tex] is
[tex] A = wl [/tex]
In this case, we know that the width is one-fourth of its length, which means [tex] w = \frac{1}{4}l[/tex]
If we plug this expression for w in the formula for the area, we get
[tex] A = wl = \dfrac{1}{4}l\cdot l = \dfrac{1}{4}l^2 [/tex]
We also know that the area is 9 squared units, so we have
[tex] 9 = \dfrac{1}{4}l^2 [/tex]
If we multiply both sides by 4, we get
[tex] l^2 = 36 [/tex]
Consider the square root of both sides (we only accept the positive solution, since a negative length would make no sense:
[tex] l = \sqrt{36} = 6 [/tex]
So, the length is 6, and the width is one-fourth of 6, i.e.
[tex]\dfrac{1}{4} \cdot 6 = \dfrac{6}{4} = \dfrac{3}{2} = 1.5[/tex]
