The width of a rectangle is 3 less than 2 times the length. If the perimeter is 51 what is the actual length and width of the rectangle

Verified Answer :

Let \(l=length\) be length and \(w=width\)

\(w=2l-3\)

To find the perimeter add all the sides of the rectangle

\(Perimeter=w+w+l+l\)

Replacing \(w=2l-3\)

\((2l-3)+(2l-3)+l+l=51\)

\(6l-6=51\)

add to both sides 6

\(6l=51+6\)

\(6l=57\)

Divide both sides with 6

\(l=57/6 \\ l=9.5\)

\(w=2l-3 \\ w=2(9.5)-3\\ w=19-3\\ w=16\)