# SOLUTION: Ok, there is a problem in my worksheet that gives me the following information: Perimeter of the Rectangle: 68cm Area of the Rectangle: 144sq. cm and its asking for the length

Algebra ->  -> SOLUTION: Ok, there is a problem in my worksheet that gives me the following information: Perimeter of the Rectangle: 68cm Area of the Rectangle: 144sq. cm and its asking for the length      Log On

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 Question 279050: Ok, there is a problem in my worksheet that gives me the following information: Perimeter of the Rectangle: 68cm Area of the Rectangle: 144sq. cm and its asking for the length of the diagonal, how do i solve this? it does not give any dimensions (Width, Height) If you can help me, id love it. Thank You Found 2 solutions by scott8148, ankor@dixie-net.com:Answer by scott8148(6628)   (Show Source): You can put this solution on YOUR website!2L + 2W = 68 ___ L + W = 34 L * W = 144 by Pythagoras, D^2 = L^2 + W^2 = (L + W)^2 - 2 LW D^2 = 34^2 - 2(144) D = sqrt(868) Answer by ankor@dixie-net.com(16523)   (Show Source): You can put this solution on YOUR website!gives me the following information: : Start by using L for Length, W for width : Perimeter of the Rectangle: 68cm 2L + 2W = 68 Simplify, divide by 2 L + W = 34 or W = (34-L) : Area of the Rectangle: 144sq. cm L * W = 144 Substitute (34-L) for W L * (34-L) = 144 34L - L^2 = 144 Arrange as a quadratic equation -L^2 + 34L - 144 = 0 We have to solve this using the quadratic formula In this equation: x=L; a=-1; b=34; c=-144 : : Two solutions L = L = +4.958 and L = L = +29.0415 : the larger 29.0415 cm is the length the smaller 4.958 cm is the width : Check our solution by finding the perimeter with a calc 2(29.0415) + 2(4.958) = 67.999 ~ 68 : and its asking for the length of the diagonal, now we have the dimensions: Use pythag for this: c = , : c = c = 29.462 is the diagonal