Question

The length of a rectangle is 3 m less than twice the width if the area of the rectangle is 66 5 m² find the dimensions

Answer 1

Let the width be x.

Then,Length = ( 2x - 3 ) m

According to the question,

Area of rectangle = 665 m² [ Given ]

Formula: Area of rectangle = Length × Width

$\sf \implies \: length \: \times breadth = 665 \: m {}^{2}$

$\sf\implies \: (2x - 3) \times x = 665$

$\sf \implies \: 2 {x}^{2} - 3x = 665$

$\sf \implies \: {2x}^{2} - 3x - 665 = 0$

By split middle term

$\sf \implies \: 2 {x}^{2} - 38x + 35x - 665 = 0$

$\sf\implies \: 2x(x - 19) + 35(x - 19) = 0$

$\sf \implies \: (2x + 35) = 0 \: or \: (x - 19) = 0$

$\sf \implies \: x = \dfrac{ - 35}{2} \: or \: \: x = 19 \:$

Note: Ignore negative number.

Now,

Width of a rectangle = 19 m

Length of a rectangle = 2x - 3 = 2 × 19 - 3 = 38 - 3 = 35 m