Question

how many tiles whose length and breadth are 12 cm and 5cm respectively will be needed to fit in a rectangular region whose length and breadth are respectively:
a. 100 cm and 144 cm
b. 70 cm and 36 cm

Answer 1

        $\text{Length of tile}(l) = 12 \: cm$

        $\text{Breadth of tile}(b) = 5 \: cm$

        $\text{We know that area of rectangle} = \text{Length}\times \text{Breadth}$

$\implies \text{Area occupied by one tile}(a) = l \times b = 12 \times 5 = 60 \: cm^2$

    $\text{a) Length and breadth of room are }L = 100 \: cm \text{ and }B = 144 \: cm$

$\implies \text{Area of room}(A) = L \times B = 144 \times 100 = 14400 \: cm^2$

$\implies \: \text{Number of tiles that can fit the room}(n) = \dfrac{A}{a}$

$\implies \: \boxed{n = \dfrac{A}{a} = \dfrac{14400}{60} = 240 \: tiles}$

    $\text{b) Length and breadth of room are }L = 70 \: cm \text{ and } B = 36 \: cm$

$\implies \: \text{Area of room}(A) = L \times B = 70 \times 36 = 2520 \: cm^2$

$\implies \: \text{Number of tiles that can fit the room}(n) = \dfrac{A}{a}$

$\implies \: \boxed{n = \dfrac{A}{a} = \dfrac{2520}{60} = 42 \: tiles}$