The length of a rectangle is 3ft more than twice the width, and the area of the rectangle is 54ft^2. Find the dimensions of the rectangle.
2 answers:
Let wedth = x Length = 2x+3 Area = 54 Area = l X b 54= (2x + 3) X x 54 = 2 x² + 3x The equation will be: 2 x² + 3x - 54 2 x² + 12x -9x - 54 2x (x+6) -9(x + 6) (2x-9) (x+6) We will use (2x-9) 2x-9= 0 2x = 9 x = 9/2 x = 4.5 Width = 4.5 Length = (2x +3) Length = (2X 4.5 + 3) Length = 9.0 + 3 = 12
Answer: Let length = 2x + 3
Let width = x
Area = 54 ft2
length × width = Area
x(2x + 3) = 54
2x2 + 3x = 54
2x2 + 3x - 54 = 0
(2x - 9)(x + 6) = 0
x = 9/2 and x = -6
x = 4.5 and x = -6
We accept x = 4.5 because length cannot be a negative value. Substituting this value into the dimensions:
width = 4.5 ft
length = 2(4.5) + 3 = 9 + 3 = 12 ft
Step-by-step explanation:
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