Question

The figure shows the dimensions of a wall having a window and a door of a room. Write an algebraic expression for the area of the wall to be painted.

Answer 1

We have a wall of dimension 5x × (5x + 2) having a window and a door of dimension (2x × x) and (3x × x), respectively.

Then, area of the window = 2x × x = 2x² sq.units

Area of the door = 3x × x = 3x² sq.units

And area of wall = (5x + 2) × 5x = (25x² + 10x) sq.units

Now, area of the required part of the wall to be painted

= Area of the wall – (Area of the window + Area of the door)

= 25x² + 10x – (2x² + 3x²)

= 25x² + 10x – 5x²

= 20x² + 10x

= 2 × 2 × 5 × x × x + 2 × 5 × x

= 2 × 5 × x(2x + 1)

= 10x(2x + 1) sq.units