Question

4. A verandah of width 2.25 m is constructed all along outside a room which is 55 m
long and 4 m wide. Find:
(i) the area of the verandah.
(ii) the cost of cementing the floor of the verandah at the rate of 200 per m.​

Answer 1

Answer:-

Given:-

→A verandah of width 2.2 m is constructed all along outside a room which is 5.5 m

→Long and 4 m  wide

We have to find:-

→(i) The area of the verandah

→(ii) The cost of cementing the floor of the verandah at the rate of 200 per m

Solution:-

(i) The area of the verandah ?

Here,

Area of verandah = Area of larger rectangle - Area of smaller rectangle

Smaller rectangle:-

Length of the smaller rectangle = 5.5 m

Breadth of the smaller rectangle = 4 m

Larger rectangle:-

2.25 m of verandah has been constructed all around outside of smaller rectangle

∴Length of larger rectangle = length of the smaller rectangle + 2 × 2.5

》$\small{5.5+2(\frac{225}{100})}$

》$5.5 + \frac{450}{100}$

》$\frac{55}{10}+\frac{45}{10}$

》$\frac{55+45}{10}$

》$\frac{100}{10}$

》$\underline{10m}$

∴Breadth of the larger rectangle = breadth of the smaller rectangle + 2 × 2.5

》$4+2(\frac{225}{100})$

》$4+\frac{450}{100}$

》$4+\frac{45}{10}$

》$\frac{4×10+45}{10}$

》$\frac{40+45}{10}$

》$\frac{85}{10}$

$》$$\underline{8.5 m}$

Larger rectangle:-

Length = l = 10m

Breadth = b = 8.5 m

Area of larger rectangle ⇒ l × b

                                        ⇒ 10×8.5

                                        ⇒10×85/10

                                        ⇒$\boxed{85m^{2}}$

Smaller rectangle:-

Length = l = 5.5 m

Breadth = b =4 m

Area of smaller rectangle ⇒l× b

                                          ⇒5.5×4

                                          ⇒55/10×4

                                          ⇒55/2×2

                                          ⇒11×2=$\boxed{22m^{2}}$

Now,

Area of verandah = Area of larger rectangle - Area of smaller rectangle

》85-22

》63m²

Therefore, Area of verandah is " 63m²"

(ii) The cost of cementing the floor of the verandah at the rate of 200 per m ?

Cost of cementing verandah in 1m²=RS.200

Cost of cementing verandah in 63m²=RS. 200×63

》RS.12,600

Therefore, It will cost "RS. 12,600" for it's cementing..

Answer 2

★Given:-

• A veranda of width 2.25 m is constructed all along outside a room which is 55m long and 4 m wide.

★To find:-

• (i) the area of the veranda.
• (ii) the cost of cementing the floor of the veranda at the rate of 200 per m.

★Solution:-

Given that 2.25 m of veranda has been constructed all along outside of a room.

Therefore,

Length of room with veranda:-

➺5.5+2.25+2.25

➺5.5+2(2.25)

➺10m

Width of room with veranda:-

➺4 + 2.25+2.25

➺4 + 2(2.25)

➺8.5m

Using the formula,

✦Aʀᴇᴀ=Lᴇɴɢᴛʜ×ᴡɪᴅᴛʜ

Putting values,

Area of room = l×b

➺ 5.5×4

➺ 22m²

Area of room with veranda:-

➺l × b

➺10×8.5

➺85m²

➲Area of the veranda = Area of room with veranda- Area of room

➺ 85 - 22

➺ 63m²

➲Cost of cementing = Area × Rate

We have,

• Area =  63m²
• Rate = 200 per m

Putting values,

➺63 × 200

➺Rs.12600.

Therefore,

➲The area of veranda is 63m²

➲The cost of cementing is Rs.12600.

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