Question

the floor of a rectangular hall has a perimeter 300m if the cost of white washing the four walls at the rate of rs10 per m² is 18000 find the height of the hall​

Answer 1

Answer :-

✧ The height of the hall = 9 metres

Given :-

◍ Perimeter of the rectangular hall = 300 m

◍ Cost of washing the four walls at the rate of Rs. 10 per m² = Rs. 18000

To find :-

→ The height of the hall

Solution :-

Let the length of the hall be l metres, breadth be b metres and height be h metres.

$= > \tt{Perimeter \: \: of \: \: the \: \: floor \: \: of \: \: the \: \: hall = 2(length + breadth)} \\ \\ = > \tt{300 m = 2(l + b)} \\ \\ = > \tt{ \dfrac{300 \: m}{2} = (l + b)}\\ \\ = > \tt{ 150 \: m = l + b \: \: \: \: \: \: \:.... eq. \: i.}$

• Area of cuboid = 2(lb + bh + lh)

• Area of floor = l × b = lb

• Area of the ceiling = l × b = lb

$\tt{=> \: Area \: \: of \: \: the \: \: four \: \: walls = Area \: \: of \: \: cuboid - Area \: \: of \: \: floor - Area \: \: of \: \: the \: \: ceiling}\\ \\ \tt{=> \: Area \: \: of \: \: the \: \: four \: \: walls = 2(lb + bh + lh) - (lb) - (lb)} \\ \\ \tt{ = 2(lb) + 2(bh) + 2(lh) - 2(lb)} \\ \\ \tt{ = 2(bh) + 2(lh)} \\ \\ \tt{ = 2h(b+l)} \\ \\ \tt{ = 2h \times (150 \: m)} \: \: \: \: \: \: ... \: from \: eq.i. \\ \\ \tt{ = 300 \: h \: {m}^{2} }$

• Area of four walls = 300 h m²

$\tt{=> \: Cost \: \: of \: \: painting \: \: the \: \: walls \: \: per \: 1 \: {m}^{2} = Rs. 10} \\ \\ \tt{=> \: Cost \: \: of \: \: painting \: \: 300 \: {m}^{2} \: \: area = Rs. 10\times 300 h} \\ \\ \tt{=> \: Rs. \: 18000 = Rs. \: 10\times 300 \: h} \\ \\ \tt{=> \: Rs. \: 18000 = Rs. \: 3000 \: h }\\ \\ \tt{=> \: \frac{Rs. \: 18000}{Rs. \: 3000} = h} \\ \\ \tt{=> \: 9 = h}$

Therefore, the height of the hall = 9 metres

More Information :-

✧ Circumference of the circle = π × diameter

Diameter = 2 × radius

So,

Circumference of the circle= 2 × π × radius

✧ Perimeter of square = 4 × side of square

✧ Area of square = (side of square)²

✧ Perimeter of the rectangle = 2(Length + Breadth)

✧ Area of the rectangle = Length × Breadth