a rectangle has a length that is 2 less than 3 times the width. if the area of this rectangle is 16 , find the dimensions and the perimeter
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a rectangle has a length that is 2 less than 3 times the width. if the area of this rectangle is 16 , find the dimensions and the perimeter
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Let the width(b) of the rectangle be 'x'.
Length, l = 3x - 2
Area of the rect. = l × b
16 = (3x - 2)*x
16 = 3x^2 - 2x
the equation is 3x^2 - 2x - 16 = 0
Now we will factorise this equation:-
3x^2 - 2x - 16
3x^2 - 8x + 6x - 16
3x^2 + 6x - 8x - 16
3x(x + 2) -8(x + 2)
(3x - 8)(x + 2)
Hence possible values of x can be 8/3 or -2.
Since the breadth can't be negative,
x = 8/3
Now, 3x - 2 = 3*(8/3) - 2
= 8 - 2 = 6 cm
Now, perimeter, P = 2(l + b)
P = 2(6 + 8/3)
P = 2(18 + 8/3)
P = 26/3 × 2
P = 52/3 cm
Hence the perimeter of the rectangle is 52/3 cm.
Thank You