Respuesta :
So let's use x for the width of the rectangle and y for its length. We know that the length is 1ft grater than the width. This means that the length is equal to the width plus 1 ft:
[tex]y=x+1[/tex]The perimeter is composed of two lengths and 2 widths which means that the sum of these four sides must be equal to 82:
[tex]82=2x+2y[/tex]We can substitute y with the expression we found before:
[tex]\begin{gathered} 82=2x+2y=2x+2\cdot(x+1) \\ 82=2x+2x+2 \\ 82=4x+2 \end{gathered}[/tex]Know that we have the equation we can find x and y. We can start by substracting 2 from both sides:
[tex]\begin{gathered} 82-2=4x+2-2 \\ 80=4x \end{gathered}[/tex]Then we divide both sides by 4:
[tex]\begin{gathered} \frac{80}{4}=4x \\ 20=x \end{gathered}[/tex]So the width is 20 ft long. Then the length y is given by:
[tex]\begin{gathered} y=x+1=20+1 \\ y=21 \end{gathered}[/tex]So the length is 21 ft. Then the answers to the boxes in order are:
82=2x+2(x+1)
x=20
y=21
