Question

10. How many tiles whose length and breadth are 12 cm and 5 cm respectively will be needed
to fit in a rectangular region whose length and breadth are respectively:
(a) 200 cm and 144 cm
(b) 80cm and 48cm​

Answer 1

SOLUTION :

➥ Given :-

• Length of a tile = 12 cm

• Breadth of a tile = 5 cm

➥ To Find :-

How many titles will be needed to fit in a rectangle region whose length and breadth are respectively

• (a) 200 cm and 144 cm

• (b) 80 cm and 48 cm

➥ Required Formula :-

$\bigstar \: \: \boxed{ \bold{ \: Area \: \: of \: \: a \: \: Rectangle = Length \times Breadth \: }}$

❖ Calculation of area of a tile :-

• Length, l = 12 cm

• Breadth, b = 5 cm

$\sf{ \large{\therefore \: \: Area = l \times b }} \: \: \: \: \: \: \: \: \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf {\large{= 12 \times 5 \: cm {}^{2} }} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ \large{= 60 \: cm {}^{2} }}$

(a)

❖ Calculation of the rectangular region :-

• Length, l₁ = 200 cm

• Breadth, b₁ = 144 cm

$\sf{ \large{ \therefore \: \: Area = l_1 \times b_1}} \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ \large{ = (200 \times 144 )\: cm {}^{2} }} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ \large{ = 28800 \: cm {}^{2} }} \: \: \:$

❖ Calculation of number of tiles required :-

$\bigstar \: \: \sf{No. \: \: of \: \: tiles = \dfrac{Area \: \: of \: \: rectangular \: \: region }{Area \: \: of \: \: a \: \: tile} } \\ \\ \sf{ = \dfrac{28800 \: cm {}^{2} }{60 \: cm {}^{2} }} \\ \\ \sf{ = 480} \: \: \: \: \: \: \: \: \: \: \:$

• Hence, the required number of tiles needed to fit the rectangular region is 480.

$\underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }$

(b)

❖ Calculation of the rectangular region :-

• Length, l₂ = 80 cm

• Breadth, b₂ = 48 cm

$\sf{ \large{ \therefore \: \: Area = l_2 \times b_2}} \: \: \: \: \: \: \: \: \: \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ \large{ = (80 \times 48) \: cm {}^{2} }} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ \large{ = 3840 \: cm {}^{2} }} \: \: \:$

❖ Calculation of number of tiles required :-

$\bigstar \: \: \sf{No. \: \: of \: \: tiles = \dfrac{Area \: \: of \: \: rectangular \: \: region }{Area \: \: of \: \: a \: \: tile} } \\ \\ \sf{ = \dfrac{3840 \: cm {}^{2} }{60 \: cm {}^{2} }} \: \: \: \\ \\ \sf{ = 64} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

• Hence, the required number of tiles needed to fit the rectangular region is 64.

$\underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }$

ANSWER :

• (a) 480 tiles will be needed whose length and breadth are 12 cm and 5 cm respectively to fit in a rectangular region whose length and breadth are 200 cm and 144 cm respectively.

• (b) 64 tiles will be needed whose length and breadth are 12 cm and 5 cm respectively to fit in a rectangular region whose length and breadth are 80 cm and 48 cm respectively.

Answer 2

Answer:

So, 42 tiles required for rectangular region.