Question

A rectangle has a length 5 meters more than five times the

Answer 1

Given:

A rectangle has a length 5 meters more than five times the  width.

The area of the rectangle is less than 100 meters  squared.

To find:

The expression or inequality that represents all possible  widths of the rectangle.

Solution:

Let x be the width of the rectangle.

Length of the rectangle is 5 meters more than five times the  width.

$length=5x+5$

Area of rectangle is

$Area=length \times width$

$Area=(5x+5) \times x$

$Area=5x^2+5x$

The area of the rectangle is less than 100 meters  squared.

$5x^2+5x$

$5x^2+5x-100$

Divide both sides by 5.

$x^2+x-20$

$x^2+5x-4x-20$

$x(x+5)-4(x+5)$

$(x+5)(x-4)$

It is true if one factor is negative and other is positive. So,

$x-4$     ...(i)

$x+5>0\Rightarrow x>-5$       ...(ii)

Using (i) and (ii), we get

$-5$

Therefore, the required expression or inequality for possible

widths of the rectangle is $-5$.