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

The expression to represent the length would be x-16/x +x/4+1.

Answer 2

The expression for length of the rectangle is $\frac{4(x-4)}{x}$.

What is a rectangle?

'A Rectangle is a four sided-polygon, having all the internal angles equal to 90 degrees. The two sides at each corner or vertex, meet at right angles.'

According to the given problem,

Let the length of the rectangle be l

Width of the rectangle = $\frac{x}{4} + 1$

Area of the rectangle = $x - \frac{16}{x}$

We know,

Area of a rectangle = length × width

⇒ $x - \frac{16}{x}$ = l × ( $\frac{x}{4} + 1$ )

⇒ $\frac{x^{2} -16}{x}$ = l × ( $\frac{x+4}{4}$ )

⇒ $\frac{4(x^{2} -16)}{x(x+4)}$ = l

⇒$\frac{4(x+4)(x-4)}{x(x+4)}$ = l

⇒ l =  $\frac{4(x-4)}{x}$

Hence we can conclude that the length of the rectangle is $\frac{4(x-4)}{x}$.

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