The length of a rectangle is 3yd more than twice the width, and the area of the rectangle is 54yd^2. find the dimensions of the rectangle.
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length = 2x+3 yard
width = x yard
area = 54 square yard = x yard × 2x+3 yard = 2x^2 + 3x = 54
2x^2 + 9x - 6x - 54 = 0
x(2x + 9) - 6(x + 9) = 0
x = -9 or x = 6
since length and breadth cannot be negative
therefore x = 6 yard
length = 15 yards
breadth = 6 yards
width = x yard
area = 54 square yard = x yard × 2x+3 yard = 2x^2 + 3x = 54
2x^2 + 9x - 6x - 54 = 0
x(2x + 9) - 6(x + 9) = 0
x = -9 or x = 6
since length and breadth cannot be negative
therefore x = 6 yard
length = 15 yards
breadth = 6 yards
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