Let the length be x units Width of a rectangle measure one-fourth less than its length = x-x/4 = 3x/4 Diagonal = sqrt( length^2 + width^2) = sqrt (x^2 +(3x/4)^2 ) = 40 sqrt (x^2 +(3x/4)^2 ) = 40 Squaring both sides x^2 + (9/4)x^2 = 1600 13x^2/4 = 1600 x^2 = 1600*4/13 = 492.307 length =x= sqrt(492.307) =22.18; width = 3x/4 = 16.64 units Length = 22.18 units and Width =16.64 units Solution Let the length be x units Width of a rectangle measure one-fourth less than its length = x-x/4 = 3x/4 Diagonal = sqrt( length^2 + width^2) = sqrt (x^2 +(3x/4)^2 ) = 40 sqrt (x^2 +(3x/4)^2 ) = 40 Squaring both sides x^2 + (9/4)x^2 = 1600 13x^2/4 = 1600 x^2 = 1600*4/13 = 492.307 length =x= sqrt(492.307) =22.18; width = 3x/4 = 16.64 units Length = 22.18 units and Width =16.64 units.