Question

The length of a rectangle is 3 cm less than its width what are the dimensions of the rectangle if its area is 270 cm²

Answer 1

Given:

The length of a rectangle is 3 cm less than its width.

The area of the rectangle is 270 cm².

To find:

The dimensions of the rectangle.

Solution:

Let x be the width of the rectangle. Then,

$\text{Length}=x-3$

Area of a rectangle is:

$\text{Area}=\text{Length}\times \text{width}$

$270=(x-3)(x)$

$270=x^2-3x$

$0=x^2-3x-270$

Splitting the middle term, we get

$x^2-18x+15x-270=0$

$x(x-18)+15(x-18)=0$

$(x-18)(x+15)=0$

$x=18,-15$

Width of the rectangle cannot be negative. So, the only value of x is 18.

$Width=18$

$Length=18-3$

$Length=15$

Therefore, the length of the rectangle is 15 cm and the width of the rectangle is 18 cm.