Question

use the rectangle diagram at the right.Write and solve an inequality to find the value of x for which the perimeter of the rectangle is less than 120.

Answer 1

The perimeter is the sum of all the sides of a geometric figure, so

`\begin{gathered} (x+4)+x+(x+4)+x<120 \\ x+4+x+x+4+x<120 \\ 4x+8<120 \end{gathered}`

To resolve this inequality you can first subtract 8 from both sides

`\begin{gathered} 4x+8-8<120-8 \\ 4x<112 \end{gathered}`

Then you divide by 4 on both sides of the inequality

`\begin{gathered} (4x)/(4)<(112)/(4) \\ x<28 \end{gathered}`

Therefore, for the perimeter of the rectangle to be less than 120, its shortest side must measure less than 28.