Question

the area of a rectangle is x-16/x. If the width of a rectangle is x/4+1, find an expression to represent the length.

Answer 1

Answer:

The expression to represent the length

• $length=\frac{4\left(x-4\right)}{x}$                      

Step-by-step explanation:

Given

• Area = x-16/x

• Width = x/4+1

• Length =?

We know that The formula for the area of the rectangle is:

• Area =  Length x Width

Thus, the length of a rectangle

Length = Area ÷ Width

            $=\frac{x-\frac{16}{x}}{\frac{x}{4}+1}$

            $=\frac{x-\frac{16}{x}}{\frac{x+4}{4}}$

            $=\frac{\frac{x^2-16}{x}}{\frac{x+4}{4}}$

$\mathrm{Divide\:fractions}:\quad \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot \:d}{b\cdot \:c}$

             $=\frac{\left(x^2-16\right)\cdot \:4}{x\left(x+4\right)}$

             $=\frac{\left(x+4\right)\left(x-4\right)\cdot \:4}{x\left(x+4\right)}$

Cancel the common factor: (x+4)

            $=\frac{4\left(x-4\right)}{x}$

Thus, the expression to represent the length

• $length=\frac{4\left(x-4\right)}{x}$