Question

A rectangles width is one-fourth of its length . its area is 9 square units

Answer 1

Answer:

Length = 6

Width = 3/2

Step-by-step explanation:

You can choose to go about this question in lots of different ways, but this is how i did it. I drew a diagram of the rectangle and labeled it: the height/length as x and the width as x/4 (they told us the width is a quarter of the length). They also told us that the area is 9 square units.

We know that length x width = area

So: length x width = 9

I'm gonna bring in the variables i used in the diagram, so:

$x$ x $\frac{x}{4}$ = 9

Keep solving:

$\frac{x^{2} }{4}$= 9

Times both sides by 4:

$x^{2}$ = 36

Square root both sides for x:

* remember that when you square root, its possible to have a positive or negative version of the value

x = ±6

Since its impossible to have a negative length, we can say that x = 6.

X was just the variable we gave to the length of the rectangle, so now we know the length is 6. If you needed to find width as well, you can do 6/4, which simplifies to 3/2.

To double-check

- 6 x 3/2 should equal 9, since length x width = area

which it is, so we're correct!

Hope that helped : )