# SOLUTION: Hi! A circular piece of sheet metal has a diameter of 20 in. The edges are to be cut off to form a rectangle of area 180 in^2 (see the figure). What are the dimensions of the re

Algebra ->  Algebra  -> Systems-of-equations -> SOLUTION: Hi! A circular piece of sheet metal has a diameter of 20 in. The edges are to be cut off to form a rectangle of area 180 in^2 (see the figure). What are the dimensions of the re      Log On

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 Question 200168: Hi! A circular piece of sheet metal has a diameter of 20 in. The edges are to be cut off to form a rectangle of area 180 in^2 (see the figure). What are the dimensions of the rectangle? thank you for your help!Answer by ankor@dixie-net.com(15746)   (Show Source): You can put this solution on YOUR website!A circular piece of sheet metal has a diameter of 20 in. The edges are to be cut off to form a rectangle of area 180 in^2 (see the figure). What are the dimensions of the rectangle : Let a = the length Let b = the width The diameter of 20" = the diagonal of the rectangle : a^2 + b^2 = 20^2; pythag a^2 + b^2 = 400 : Area of the rectangle a * b = 180; the area of the rectangle b = : Substitute (180/a) in the pythag equation a^2 + ()^2 = 400 : a^2 + = 400 Multiply equation by a^2: a^4 + 32400 = 400a^2 Arrange as a quadratic equation a^4 - 400a^2 + 32400 = 0 : Use the quadratic formula in this equation a=1, b=-400, c=32400; solve for x^2 : : Two solutions x^2 = 287.178 x = x = 16.946" the length of the rectangle (a) and : x^2 = 112.827 x = x = 10.622" the width of the rectangle (b) : The rectangle is: 16.946 by 10.622 : Check this by finding the area with these values 16.946 * 10.622 = 180.00 sq/in : Find the diameter/diagonal on a calc using these values; enter: d = d = 20.02 ~ 20"