Question

Find the area of a rectangle that has a length of 2x+3 and width of x. Some one painted an area inside the rectangle that has a length of 3 and a width of x-2. Find the area that was NOT painted.?

Answer 1

`color(orange)("Area of NOT painted portion " = color(brown)(2x^2 + 6 = 2 * (x^2 + 3)`

Explanation:

`"Area of bigger rectangle " ABCD = (2x + 3) * x = 2x^2 + 3x`

`"Area of painted rectangle " EFGH = 3 * (x - 2) = 3x - 6`

`"Area of NOT painted portion "= Area ABCD - Area EFGH`

`"Area of NOT painted portion " = 2x^2 + 3x - 3 * (x - 2) = 2x^2 + 6 = 2 * (x^2 + 3)`