Question

The length of a rectangle is 3 inches less than 7 times its width. If the perimeter is 58 inches, find the width of the rectangle.

Answer 1

→ Let the width of the rectangle = x inches

∵ The length of the rectangle is 3 less than 7 times the width

∴ The length of the rectangle = 7(x) - 3

→ The perimeter of the rectangle P = 2(length + width)

`\begin{gathered} \because P=2(7x-3+x) \\ \therefore P=2(8x-3) \\ \therefore P=2(8x)-2(3) \\ \therefore P=16x-6 \end{gathered}`

∵ The perimeter is 58 inches

`\therefore16x-6=58`

→ Add 6 to both sides

`\begin{gathered} \because16x-6+6=58+6 \\ \therefore16x=64 \end{gathered}`

→ Divide both sides by 16 to find x