SOLUTION: In a rectangle, the length is 2 times the width. If the length and the width both increase by 3 cm, the area will increase by 54 cm2. How long are the length and the width? from Mi
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Question 416916: In a rectangle, the length is 2 times the width. If the length and the width both increase by 3 cm, the area will increase by 54 cm2. How long are the length and the width? from Michael(5th grade) Answer by sudhanshu_kmr(1152) (Show Source):
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let width =x, length = 2x
area = 2x * x = 2x^2
after increasing length and width, area = (x+3)(2x+3)
(x+3)*(2x+3) = 54 + 2x^2
=> 2x^2 + 9x + 9 = 54 + 2x^2
=> 9x = 54-9 = 45
=> x = 5
so, width = 5 cm , length = 10 cm
