# SOLUTION: Solve using a system of two equations and two unknowns. A computer parts company wants to make a rectangular memory board that has a perimeter of 28 centimeters and a diagonal leng

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 Question 633177: Solve using a system of two equations and two unknowns. A computer parts company wants to make a rectangular memory board that has a perimeter of 28 centimeters and a diagonal length of 10 centimeters. Find the dimensions of the board. Consider the length to be the longer side.Answer by ankor@dixie-net.com(15746)   (Show Source): You can put this solution on YOUR website!Solve using a system of two equations and two unknowns. A computer parts company wants to make a rectangular memory board that has a perimeter of 28 centimeters and a diagonal length of 10 centimeters. Find the dimensions of the board. Consider the length to be the longer side. : Call the two sides L & W : the perimeter 2L + 2W = 28 Simplify, divide by 2 L + W = 14 L = (14-W); use this form for substitution : The hypotenuse, (diagonal) L^2 + W^2 = 10^2 L^2 + W^2 = 100 : Replace L with (14-W) (14-W)^2 + W^2 = 100 ; FOIL (14-W)*(14-W) 196 - 28W + W^2 + W^2 = 100 2W^2 - 28W + 196 - 100 = 0 : A quadratic equation 2W^2 - 28W + 96 = 0 : Simplify, divide by 2 W^2 - 14W + 48 = 0 : Factors to (W-6)(W-8) = 0 : Two solutions W = 6 and W = 8 Make W = 6 cm as the width, then L = 8 cm as the length : : Check our solution on a calc, find the hypotenuse: Results: 10