Question

The formula for the perimeter P of a rectangle with length L and width w is P = 2(L+W). Find the length of the rectangle shown here if the perimeter is 9 and 1/2 feet. Solve the equation for L and justify each step.

Answer 1

L =
`(P - 2W)/(2)` and L = 3
`(1)/(2)`

distribute the bracket on the right side of the formula

P = 2L + 2W

subtract 2W from both sides

P - 2W = 2L

divide both sides by 2

L =
`(P - 2W)/(2)`

solve for L for P =
`(19)/(2)` and W =
`(5)/(4)`

L = (
`(19)/(2)` -
`(5)/(2)`)/2 =
`(7)/(2)` = 3
`(1)/(2)`