Question

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

Answer 1

Answer:

Let width of the rectangle be x

Length = 3x-2

Area of rectangle = Length * Breadth

(3x-2)(x)=16

3x²-2x=16

3x²-2x-16=0

3x²+6x-8x-16=0

3x(x+2)-8(x+2)=0

(x+2)(3x-8)=0

x=-2, 8/3

Width cannot be negative

So width = 8/3 unit

Length = 3x-2 = 3(8/3)-2 = 6 unit

Perimeter = 2(Length + Width) = 2(8/3+6) = 52/3 units