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 mº?
​

Answer 1

◐ Given ◑

A flooring tile in the shape of a rhombus has diagonals of length 60 cm and 80 cm

◐ To find ◑

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

◐ Solution ◑

$\\\bold\dag\:{\sf{\purple{Diagonals\:of\:rhombus=60cm\:and\:80cm}}}$

$\bold\dag\:{\sf{\purple{Area\:of\:floor=360m^2}}}$

• 1 m = 100 cm

• D1 = 60 m = 60/100 = 0.6 m

• D2 = 80 m = 80/100 = 0.8 m

$\\\bigstar\:{\sf{\red{Area_{(rhombus)}=Area_{(1\:tile)}}}}$

$\\\qquad\large{\underline{\mathfrak{\orange{\qquad As\:we\:know\:that\qquad}}}}$

${\underline{\boxed{\bf{Area\:of\:rhombus\:= \dfrac{1}{2}\times product\:of\: diagonals}}}}$

• Put all the values

$\\\implies\sf \dfrac{1}{2}\times D_1 \times D_2$

$\implies\sf \dfrac{1}{2}\times 0.6 \times 0.8$

$\implies\sf 0.3 \times 0.8$

$\implies\sf 0.24m^2$

$\therefore{\underline{\tt{Area\:of\: one\:tile \:is\: \bf 0.24m^2}}}$

$\:$____________________________________________

$\qquad{\bf{\red{Area\:of\:floor=360m^2}}}$

$\qquad\sf \dfrac{Area\:of\:floor}{Area\:of\:one\:tile}$

• Substitute all the values

$\implies\sf \dfrac{360}{0.24}$

$\implies\sf \cancel\dfrac{360}{24}\times 100$

$\implies\sf 15\times 100$

$\implies\sf 1500 \: tiles$

$\bullet\:{\underline{\boxed{\sf{Number\:of\:tiles\: required=2400\:tiles}}}}$

$\:$____________________________________________

Answer 2

Answer:

Given :-

• A flooring tile in the shape of a rhombus has diagonals of length 60 cm and 80 cm.

To Find :-

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

Formula Used :-

${\red{\boxed{\large{\bold{Area\: of\: Rhombus =\: \dfrac{d_1 \times d_2}{2}}}}}}$

where,

• d₁ = One diagonal
• d₂ = Other diagonal

Solution :-

First we have to convert cm to m,

As we know that,

✧ 1 cm = 1/100 m ✧

Then,

● d₁ = 60 cm = $\sf \dfrac{60}{100}$ = 0.6 m

● d₂ = 80 cm = $\sf \dfrac{80}{100}$ = 0.8 m

Again, we have to find the area of one tiles,

Given :

• d₁ = 0.6 m
• d₂ = 0.8 m

According to the question by using the formula we get,

⇒ $\sf Area\: of\: rhombus =\: \dfrac{0.6 \times 0.8}{2}$

⇒ $\sf Area\: of\: rhombus =\: \dfrac{6 \times 8}{2 \times 10 \times 10}$

⇒ $\sf Area\: of\: rhombus =\: \dfrac{\cancel{48}}{\cancel{2} \times 10 \times 10}$

⇒ $\sf Area\: of\: rhombus =\: \dfrac{24}{100}$

➦ $\sf\bold{\green{Area\: of\: rhombus =\: 0.24\: {m}^{2}}}$

Hence, area of one tiles is 0.24 m² .

Now, we have to find how many tiles will be required to cover a floor of area of 360 m²,

As we know that,

✠ $\sf Number\: of\: tiles =\: \dfrac{Area\: of\: floor}{Area\: of\: one\: tiles}$

Given :

• Area of floor = 360 m²
• Area of one tiles = 0.24 m²

According to the question by using the formula we get,

↦ $\sf Number\: of\: tiles =\: \dfrac{360}{0.24}$

↦ $\sf Number\: of\: tiles =\: \dfrac{360 \times 100}{24}$

↦ $\sf Number\: of\: tiles =\: \dfrac{\cancel{36000}}{\cancel{24}}$

➠ $\sf\bold{\purple{Number\: of\: tiles =\: 1500\: tiles}}$

$\therefore$ 1500 tiles will be required to cover a floor of area of 360 m².