Maths-

General

Easy

Question

# How many square tiles of the side 20 cm will be needed to pave a footpath which is 2 m wide and surrounds a rectangular plot 40 m long and 22 m wide.

Hint:

### Area of a rectangle = length × breadth

## The correct answer is: ∴ 6,600 tiles would be required to cover the footpath.

### Step-by-step solution:-

Paving the floor of a footpath with tiles means putting tiles on the whole surface of the footpath.

∴ If we know the area of the footpath and the area of each tile, we can find the number of tiles required to cover the footpath.

Let the number of tiles required be n

Now, from the given information,

length of the plot = l1 = 40 m

breadth of the plot = b1 = 22 m

Side of each tile = 20 cm = 0.2 m (1m = 100 cm)

∴ Area of the plot = length × breadth

∴ Area of the plot = 40 × 22

∴ Area of the plot = 880 m2 ............................................................... (Equation i)

In the adjacent diagram-

For the outer rectangle-

Length = Length of plot + 2 (width of footpath)

Length = 40 + 2 (2)

Length = 40 + 4

Length = 44 m .................................................................................. (Equation ii)

Breadth = Breadth of plot + 2 (width of footpath)

Breadth = 22 + 2 (2)

Breadth = 22 + 4

Breadth = 26 m .................................................................................. (Equation ii)

Area of Outer rectangle = length × breadth

∴ Area of Outer rectangle = 44 × 26 ..................................................... (From Equations ii & iii)

∴ Area of Outer rectangle = 1,144 m^{2} .................................................. (Equation iv)

Area of footpath = Area of outer rectangle - Area of inner plot

∴ Area of footpath = 1,144 - 880 ......................................................... (From Equations i & iv)

∴ Area of footpath = 264 m^{2} ............................................................... (Equation v)

Area of each tile = Side^{2}

∴ Area of each tile = (0.2)^{2}

∴ Area of each tile = 0.04 m^{2} ............................................................... (Equation vi)

Area of the footpath = Area of each tile × total number of tiles required.

∴ 264 = 0.04 × total number of tiles required ................... (From Equations v & vi)

∴ 264 / 0.04 = total number of tiles required

∴ 6,600 = total number of tiles required

Final Answer:-

∴ 6,600 tiles would be required to cover the footpath.

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