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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.
Solution
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
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