Question

The floor of a building consists of 3000 tiles which are rhombus shaped and each of its diagonals are 45 cm and 30 cm in length.
Find the total cost of polishing the floor, if the cost per m² is Rs. 5.


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Answer 1

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Answer 2

$\sf \bf \huge {\boxed {\mathbb {QUESTION}}}$

$\tt The\: floor\: of\: a \:building\: consists\: of\: 3000\: tiles\\\tt which\: are \:rhombus \:shaped \:and\: each \:of \:its\\\tt diagonals\: are\: 45 \:cm\: and\: 30\: cm\: in\: length.\\\tt Find\: the\: total \:cost \:of\: polishing\: the\: floor\:, if \\\tt the\: cost\: per {m}^{2}\: is\: Rs\:. 5.$

$\sf \bf \huge {\boxed {\mathbb {ANSWER}}}$

$\sf \bf {\boxed {\mathbb {GIVEN}}}$

• $\sf \bf {AC\:and\:BD\:are\: the \:diagonals}$
• $\sf \bf {AC=30\:cm}$
• $\sf \bf {BD=45\:cm}$

$\sf \bf {\boxed {\mathbb {TO\:PROVE}}}$

• $\sf \bf {3000 \:tiles \:areas\:of \:rhombus}$

• $\sf \bf Total\: cost\: of\: polishing\: the\: floor\\\sf \bf if\: the \:cost \:per\:{m}^{2} \:is\: Rs \:5.$

$\sf \bf {\boxed {\mathbb {SOLUTION}}}$

$\tt Area \:of\: 1 \:tile$

$\sf \bf \implies {d_1=45\:cm}$

$\sf \bf \implies {d_3=30\:cm}$

${\boxed{\boxed {\color{blue} {\sf \bf A= \dfrac{1}{2} \times d_1 \times d_2}}}}$

• $\sf \bf {A=Area\: of\: rhombus}$
• $\sf \bf {d_1=diagonal 1}$
• $\sf \bf {d_2=diagonal 2}$

$\tt Substitute\: the\: values$

$\sf \bf \implies {A=\dfrac{1}{2} \times 45 \times 30}$

$\sf \bf \implies {A=45 \times 15}$

$\implies {\boxed {\sf \bf A=675\:{cm}^{2}}}$

$\sf \bf {Area \:of \:3000\: tiles =3000 \times Area\: of\: 1\: tile}$

$\sf \bf \implies {3000 \times 675}$

$\implies {\boxed {\color{green} {\sf \bf Area \:of \:3000\: tiles=2025000\:{cm}^{2}}}}$

$\tt {Convertion \: {cm}^{2} \:to\: {m}^{2}}$

$\sf \bf \implies {2025000 \times {\dfrac{1}{100}}^{2}\:{m}^{2}}$

$\sf \bf \implies {2025000 \times (\dfrac{1}{10000}) \:{m}^{2}}$

$\sf \bf \implies \dfrac{2025 \cancel {000}}{10 \cancel {000}} \:{m}^{2}$

$\sf \bf \implies \dfrac{2025}{10}\:{m}^{2}$

$\implies{\boxed {\sf \bf 202.5\:{m}^{2}}}$

$\tt {Cost\: of \:polishing}$

$\sf \bf \implies Cost\: of \:polishing\:1\:tile=Rs.5$

$\sf \bf \implies Cost\: of \:polishing\:202.5\:{m}^{2}=5 \times 202.5$

$\implies {\boxed {\color {red} {\sf \bf Rs. 1012.5}}}$

$\sf \bf \huge {\boxed {\mathbb {HOPE \:IT \:HELPS \:YOU }}}$

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$\sf \bf \huge {\boxed {\mathbb {EXTRA\:INFORMATION}}}$

$\sf \bf {Area\: of\: rhombus=\dfrac{1}{2} \times d_1 \times d_2}$

$\sf \bf {Area\: of\: rectangle =l \times b}$

$\sf \bf {Area\: of\: square = {a}^{2}}$

$\sf \bf {Area\: of\: parallelogram =b \times h}$

${\mathbb{\colorbox {orange} {\boxed{\boxed{\boxed{\boxed{\boxed{\colorbox {lime} {\boxed{\boxed{\boxed{\boxed{\boxed{\colorbox {aqua} {@suraj5070}}}}}}}}}}}}}}}$