The width of a rectangle is 5 centimeters less than the length. the area is 36 square centimeters. find the length.

If the width is Wthen the length is 2W-5 W(2W-5)=422W2-5W = 422W2-5W-42 = 0 Factor by grouping or do the quadratic equation.Multiply the coefficient of the squared term.. 2..by the constant ..-42..   2(-42)=-84Factors of -84 that add to the coefficient..-5.. ofthe W term are  7(-12)Replace the -5W with  -12W + 7W 2W2-12W+7W-42 = 02W(W-6) + 7(W-6)=0(2W+7)(W-6)=0
 Either:   2W+7 = 0   or   W-6 = 0             2W = -7           W = 6 cm             W = -7/2 cm

Since W will not be a negative, our width is 6cmThe length is 2W-5 = 2(6)-5=12-5 = 7 cm