Question

⚘ Question :
A flooring tile in the shape of a rhombus has diagonals of length 80 cm and 120 cm, how many such tiles will be required to cover a floor of area 360 m²?​

Answer 1

⚘ Question :

A flooring tile in the shape of a rhombus has diagonals of length 60 cm and 80 cm, how many such tiles will be required to cover a floor of area 360 m²?

$\begin{gathered}{\textsf{\textbf{\underline{\underline{Given :}}}}}\end{gathered}$

➳A flooring tile in the shape of a rhombus has diagonals of length 80 cm and 120 cm.

$\begin{gathered}{\textsf{\textbf{\underline{\underline{To Find :}}}}}\end{gathered}$

➳ How many such tiles will be required to cover a floor of area 360 m²

$\begin{gathered}{\textsf{\textbf{\underline{\underline{ Formula required:}}}}}\end{gathered}$

$\red{\dag{\underline{\boxed{\sf{Area \: of \: Rhombus = \dfrac{1}{2} \times (D_1) \times (D_2)}}}}†}{\begin{gathered}\end{gathered}}$

$\begin{gathered}{\textsf{\textbf{\underline{\underline{Solution :}}}}}\end{gathered}$

$\red\bigstar first \: \:we \: convert \: the \: lenght \: of \: diagonals \: into \: m. \:$

$\red{we \: know \: that }\\ \implies{\sf{1 \: cm = \dfrac{1}{100} \: m}}$

$\implies{\sf{80\: cm = {\cancel\dfrac{80}{100}} = \dfrac{8}{10} \: m }}$

$\implies{\sf{120\: cm = {\cancel\dfrac{120}{100}} = \dfrac{12}{10} \: m }}$

∴ The lenght of diagonal are Rhombus is 8/10 m and 12/10 m..

$\begin{gathered}\end{gathered}\red\bigstar Area \: of \: rhombus.$

$\star{{\sf{Area \: of \: Rhombus = \dfrac{1}{2} \times (D_1) \times (D_2)}}}$

${ \star{\sf{Area \: of \: Rhombus = \dfrac{1}{2} \times \dfrac{8}{10} \times \dfrac{12}{10} }}}$

${ \star{\sf{Area \: of \: Rhombus = \dfrac{1}{2} \times 0.8\times 1.2 }}}$

${: \star{\sf{Area \: of \: Rhombus = \dfrac{1 \times 0.8 \times 1.2}{2}}}}$

${ \star{\sf{Area \: of \: Rhombus = \dfrac{0.96}{2}}}}$

${ \star{\sf{Area \: of \: Rhombus = \cancel{\dfrac{0.96}{2}}}}}$

${\star{\sf{Area \: of \: Rhombus = 0.48 \: {m}^{2}}}}:$

${\bigstar\underline{\boxed{\sf{\red{Area \: of \: Rhombus} = \purple{0.24 \: {m}^{2}}}}}}★$

★ the number of tiles will be required to cover a floor of area 360 m².

${\implies{\sf{Number \: of \: Tiles = \dfrac{Area \: of \: floor }{Area \: of \: one \: tile}}}}$

${ \implies{\sf{Number \: of \: Tiles = \dfrac{360}{0.48}}}}$

★For removing the decimal point we multiply it by 100.

${ \implies{\sf{Number \: of \: Tiles = \dfrac{360 \times 100}{0.48 \times 100}}}}$

${\implies{\sf{Number \: of \: Tiles = \dfrac{36000}{48}}}}$

${ \implies{\sf{Number \: of \: Tiles = \cancel{\dfrac{36000}{48}}}}}$

${ \implies{\sf{Number \: of \: Tiles = 750 \: Tiles}}}$

$\bigstar{\underline{\boxed{\sf{\red{Number \: of \: Tiles}= \purple{750 \: Tiles}}}}}★$

∴ 750 tile will be required to cover a floor of area 360 m².

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