Question

The length of a rectangle is three more than twice the width. Find the width and the length if the perimeter is 84 f

Answer 1

$\text{Hello! :D}$

$\boxed{\text{width = 13ft, length = 29ft}}$

$\text{ Let the width = "w":}\\\\\text{Write an expression to represent the length in terms of "w":}\\\\l = 2w + 3\\\\\text{Formula of a rectangle: } \\\\P = 2l + 2w\\\\\text{Therefore:}\\\\84 = 2(2w + 3) + 2(w)\\\\84 = 4w + 6 + 2w\\\\84 = 6w + 6\\\\\text{Subtract 6 from both sides:}\\\\78 = 6w\\\\\text{Divide both sides by 6:}\\\\78/6 = 6w/6\\\\w = 13ft\\\\\text{Plug this value of "w" into the equations for the length:}\\\\l = 2(13) + 3\\\\l = 26 + 3\\\\l = 29ft$