Question

a rectangle has a length 3 meters more than three times the width. the area of the rectangle is less than 90 meters squared. write an expression that represents all possible widths (use the variable x) of the rectangle. write your answer as an inequality, a < x < b.

Answer 1

Answer: -6<x<5

Explanation:

Given

Length is 3 m more than three times the width

Suppose width is x

So, the length is 3x+3

The area of a rectangle is
`length* width`

Area=
`(3x+3)x<90`

`\Rightarrow 3x^2+3x-90<0\\\Rightarrow x^2+x-30<0\\\Rightarrow x^2+6x-5x-30<0\\\Rightarrow (x+6)(x-5)<0\\\Rightarrow -6<x<5`