ᴀ ғʟᴏᴏʀɪɴɢ ᴛɪʟᴇ ɪɴ ᴛʜᴇ sʜᴀᴘᴇ ᴏғ ᴀ ʀʜᴏᴍʙᴜs
ʜᴀs ᴅɪᴀɢᴏɴᴀʟs ᴏғ ʟᴇɴɢᴛʜ 60 ᴄᴍ ᴀɴᴅ 80
ᴄᴍ, ʜᴏᴡ ᴍᴀɴʏ sᴜᴄʜ ᴛɪʟᴇs ᴡɪʟʟ ʙᴇ ʀᴇǫᴜɪʀᴇᴅ
ᴛᴏ ᴄᴏᴠᴇʀ ᴀ ғʟᴏᴏʀ ᴏғ ᴀʀᴇᴀ 360 ᴍº?
Answers
Answer:
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}\end{gathered}
⚘ Solution :
\begin{gathered}{\textsf{\textbf{\underline{\underline{Given :}}}}}\end{gathered}
Given :
➳ A flooring tile in the shape of a rhombus has diagonals of length 60 cm and 80 cm
\begin{gathered}\end{gathered}
\begin{gathered}{\textsf{\textbf{\underline{\underline{To Find :}}}}}\end{gathered}
To Find :
➳ How many such tiles will be required to cover a floor of area 360 m²
\begin{gathered}\end{gathered}
\begin{gathered}{\textsf{\textbf{\underline{\underline{Using Formula :}}}}}\end{gathered}
Using Formula :
\dag{\underline{\boxed{\sf{Area \: of \: Rhombus = \dfrac{1}{2} \times (D_1) \times (D_2)}}}}†
AreaofRhombus=
2
1
×(D
1
)×(D
2
)
Solution :
\red\bigstar★ Firstly converting the lenght of diagonals to m.
: \implies{\sf{1 \: cm = \dfrac{1}{100} \: m}}:⟹1cm=
100
1
m
: \implies{\sf{60\: cm = {\cancel\dfrac{60}{100}} = \dfrac{6}{10} \: m }}:⟹60cm=
100
60
=
10
6
m
: \implies{\sf{80\: cm = {\cancel\dfrac{80}{100}} = \dfrac{8}{10} \: m }}:⟹80cm=
100
80
=
10
8
m
∴ The lenght of diagonal are Rhombus is 6/10 m and 8/10 m..
\begin{gathered}\end{gathered}
\red\bigstar★ Now,Calculating the area of rhombus.
{: \longmapsto{\sf{Area \: of \: Rhombus = \dfrac{1}{2} \times (D_1) \times (D_2)}}}:⟼AreaofRhombus=
2
1
×(D
1
)×(D
2
)
Substuting the values
{: \longmapsto{\sf{Area \: of \: Rhombus = \dfrac{1}{2} \times \dfrac{6}{10} \times \dfrac{8}{10} }}}:⟼AreaofRhombus=
2
1
×
10
6
×
10
8
{: \longmapsto{\sf{Area \: of \: Rhombus = \dfrac{1}{2} \times 0.6\times 0.8 }}}:⟼AreaofRhombus=
2
1
×0.6×0.8
{: \longmapsto{\sf{Area \: of \: Rhombus = \dfrac{1 \times 0.6 \times 0.8}{2}}}}:⟼AreaofRhombus=
2
1×0.6×0.8
{: \longmapsto{\sf{Area \: of \: Rhombus = \dfrac{0.48}{2}}}}:⟼AreaofRhombus=
2
0.48
{: \longmapsto{\sf{Area \: of \: Rhombus = \cancel{\dfrac{0.48}{2}}}}}:⟼AreaofRhombus=
2
0.48
{: \longmapsto{\sf{Area \: of \: Rhombus = 0.24 \: {m}^{2}}}}:⟼AreaofRhombus=0.24m
2
⟼AreaofRhombus=
2
0.48
{: \longmapsto{\sf{Area \: of \: Rhombus = 0.24 \: {m}^{2}}}}:⟼AreaofRhombus=0.24m
2
{\bigstar\underline{\boxed{\sf{\blue{Area \: of \: Rhombus} = \purple{0.24 \: {m}^{2}}}}}}★
AreaofRhombus=0.24m
2
∴ Area of one tile is 0.24 m
\begin{gathered}\end{gathered}
\red\bigstar★ Now,Calculating 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}}}}:⟹NumberofTiles=
Areaofonetile
Areaoffloor
Substuting the values
{: \implies{\sf{Number \: of \: Tiles = \dfrac{360}{0.24}}}}:⟹NumberofTiles=
0.24
360
{: \implies{\sf{Number \: of \: Tiles = \dfrac{360 \times 100}{0.24 \times 100}}}}:⟹NumberofTiles=
0.24×100
360×100
{: \implies{\sf{Number \: of \: Tiles = \dfrac{36000}{24}}}}:⟹NumberofTiles=
24
36000
{: \implies{\sf{Number \: of \: Tiles = \cancel{\dfrac{36000}{24}}}}}:⟹NumberofTiles=
24
36000
{: \implies{\sf{Number \: of \: Tiles = 1500 \: Tiles}}}:⟹NumberofTiles=1500Tiles
\bigstar{\underline{\boxed{\sf{\blue{Number \: of \: Tiles}= \purple{1500 \: Tiles}}}}}★
NumberofTiles=1500Tiles
∴ 1500 tile will be required to cover a floor of area 360 m²..
\begin{gathered}\end{gathered}
Explanation:
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Answer:
1500 tiles
Step-by-step explanation:
Area of rhombus = 1/2 x product of diagonals
Area = 1/2 x 60x 80
Area 2400cm^2
Area = 0.24m 2
Let the number of tiles needed be x, then
x x 0.24=360
x = 1500 tiles