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Q.

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


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a

10x(2x+1)

b

10x(2x-1)

c

x(2x+1)

d

10x(x+1) 

answer is A.

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Detailed Solution

It is given that the dimensions of a wall, a window and a door of a room are given in the figure.
Question ImageWe can observe from the figure that for the wall, the given length is (5x+2) units and breadth is 5x.
Area of rectangle = Length × breadth.
For the window, the given length and breadth are 2x and x units respectively, and for the door it is 3x and x respectively.
Recognize that the area of the wall that needs to be painted is the wall's area minus the areas of the door and window.
Area of the wall = (5x+2)(5x) ⇒Area of the wall = 25 x 2 +10x  
Area of the door is,
3x×x=3 x 2  
Area of the window is,
x×2x=2 x 2  
Calculate the area of the wall to be painted by substituting all the values. Area of wall to be painted =25 x 2 +10x−3 x 2 −2 x 2 ⇒Area of wall to be painted =20 x 2 +10x ⇒Area of wall to be painted =10x(2x+1) sq units  
Area of wall to be painted is 10x(2x+1) sq units,
Hence, option 1 is correct.
 
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