Mathematics: Arectangle’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.

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Arectangle’s width is one-fourth of its length.

groundcontrol

16.01.2022

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 and length 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.

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

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