Question

A rectangle has length that is 2 less than 3 times the width. If the area of the rectangle is 16 cm square ,find the dimensions

Answer 1

Let width be x.
Length be ( 3x - 2)

Area = 16 cm²

x( 3x - 2) = 16
=> 3x² - 2x - 16 =0
=> 3x² - 6x +8x - 16 =0
=> 3x ( x - 2) + 8 ( x - 2) =0
=> ( 3x + 8) ( x - 2) =0
=> x = 2

So,

Width = 2cm
Length = 4 cm

Answer 2

Given,

A rectangle has a length that is 2 less than 3 times the width. The area of the rectangle is 16 cm square.

To find,

The dimensions of the rectangle.

Solution,

Let the width of rectangle = x

The length of the rectangle is 2 less than 3 times the width. Mathematically, it can be represented as-

Breadth of rectangle is = 3x - 2

Area of rectangle = Length × Breadth

Area of rectangle = 16cm² .

⇒   x(3x-2) = 16

⇒   3x²-2x-16=0

⇒   3x²-8x+6x-16=0

⇒   3x²+6x-8x-16=0

⇒   3x(x+2) -8(x+2)=0

⇒   x+2 = 0 and 3x-8=0

⇒   x = -2 and x = 8/3

x = -2 would be rejected because length cant be negative.

Therefore, breadth of rectangle = 8/3.

Length of rectangle ⇒ 3x-2 = 3(8/3)-2 = 6