SOLUTION: A tinsmith has two pieces of sheet metal with the same area. One is a square and the other is a rectangle 18 cm longer than the square but 9 cm less wide than the square. Find th

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Question 24604: A tinsmith has two pieces of sheet metal with the same area. One is a square and the other is a rectangle 18 cm longer than the square but 9 cm less wide than the square. Find the total area of each piece of metal.
please help
Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
let x represent unknow side.
Rectangle = x+18
Square = x-9
Since we know that the area is equivlent we muplitply them together


(x+18)(x-9)
x%5E2%2B9x-162=0
Use Quadrtic Formula:x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
in Ax%5E2%2BBx%2BC A=1, b=9, c=-162
x=%28-9%2B-sqrt%289%5E2-4%2A1%2A-162%29%29%2F%282%2A1%29%29
x=%28-9%2B-sqrt%2881%2B648%29%29%2F2%29 ---> take out the subbtraction
x=%28-9%2Bsqrt%28729%29%29%2F2%29 --> Simplify
x = 9

Hence the length of the retangle is 18+(9)=27cm and the width is 9cm.
Paul.