A room is x meters long, y meters broad and z meters high; find how many square meters of carpet will be required for the floor and how many square meters of paper for the walls? (a). xy and 2xy + 2yz (b). xy and 2xy + 2yz (c). xy and 2xy (d). xy and 2xy + 2xz
Hint: Here we have to tell the length of the carpet required for the floor which is equal to the total area of the floor, and we have to tell the dimension of the paper for the wall which is equal to the area of the four walls. Hence, after solving these we will get our required answer.
Complete step-by-step answer:
According to the given information in question we have the dimensions of the room which is x meters long y meters broad and z meters high Length = x, breadth = y, height = z The required square meter of carpet can be find using the formula of square i.e. \[Area = length \times breadth\] ………………………..(1) Substituting the given values in the equation 1 Area of the floor = \[l \times b\]=$x \times y$ So xy m2 is the area of floor To find the area of 4 walls we will use the formula \[l \times h + b \times h + l \times h + b \times h\] or 2h (l + b) Substituting the given values in the above formula Area of four walls = 2h (l+b) = 2z(x+y) $ \Rightarrow $Area of 4 walls = 2xz + 2yz Hence, option A is the correct option.
Note: In the question it is advised to remember that formula for area of square to find the area of carpet required for the floor moreover there is a very important property of the rectangle that the 2 sides of the rectangle are parallel and equal to each other. In these types of questions once you find the way to approach the solution to the problem you will understand that these types of questions can easily be solved by the basic formulas of shapes like a rectangle, square etc.
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