Question

Write and solve an inequality to determine the values that x can be so the area of the rectangle shown is at least 27 centimeters squared.

Answer 1

Given:

Width of the rectangle =3 and length of the rectangle = 4+x.

Consider the area of the rectangle.

`A=lw`

Substitute l=4+x and w=3 in the formula.

`A=3(4+x)`
`A=12+3x`
`A=3x+12`

The area of the rectangle is at least 27 centimeters squared.

`A\le27`

Substitute A=12+3x in the inequality, we get

`3x+12\le27`

The inequality is

`3x+12\le27`

Subtracting 12 from both sides of the inequalities, we get

`3x+12-12\le27-12`

`3x\le15`

Dividing both sides by 5, we get

`(3x)/(3)\le(15)/(3)`
`x\le5`

Hence the solution is

`x\le5`