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

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