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Mensuration | Mensuration Exercise 20B

Question 4

A school has a hall which is 22 m long and 15.5 m broad. A carpet is laid inside the hall leaving all-around a margin of 75 cm from the walls. Find the area of the carpet and the area of the strip left in uncovered. If the width of the carpet is 82 cm, find its cost at the rate of ₹ 60 per m.

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Let PQRS be the hall and ABCD be the carpet inside the hall.

School has a hall of length PQ = 22 m

Breadth of the hall PS = 15.5 m

∴Area of the hall PQRS = (l × b) \mathrm{m}^{2}

\begin{array}{l} =(22 \times 15.5) \\ =341 \mathrm{m}^{2} \end{array}

Carpet is laid inside the hall leaving all around a margin of =75 cm = 0.75 m

Then,

The length of the carpet, AB = (22 – (2 × 0.75)) = (22 – (1.5)) = 20.5 m

The breadth of the carpet, AD = (15.5 – (2 × 0.75)) = (15.5 – (1.5)) = 14 m

∴Area of the carpet ABCD = (20.5 \times 14) \mathrm{m}^{2}=287 \mathrm{m}^{2}

Area of the Strip = (Area of PQRS – Area of ABCD)

= (341 – 287)

=54 \mathrm{m}^{2}

Now,

Area of 1 m of carpet = 1 × 0.82 = 0.82 \mathrm{m}^{2}

∴Length of the carpet whose area 287 \mathrm{m}^{2} = 287/0.82 = 350 m

Hence cost of 350 m long carpet = ₹ (60 × 350)

= ₹ 21000

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Question 4

A school has a hall which is 22 m long and 15.5 m broad. A carpet is laid inside the hall leaving all-around a margin of 75 cm from the walls. Find the area of the carpet and the area of the strip left in uncovered. If the width of the carpet is 82 cm, find its cost at the rate of ₹ 60 per m.

Looking to do well in your science exam ? Learn from an expert tutor. Book a free class!

Let PQRS be the hall and ABCD be the carpet inside the hall.

School has a hall of length PQ = 22 m

Breadth of the hall PS = 15.5 m

∴Area of the hall PQRS = (l × b) \mathrm{m}^{2}

\begin{array}{l} =(22 \times 15.5) \\ =341 \mathrm{m}^{2} \end{array}

Carpet is laid inside the hall leaving all around a margin of =75 cm = 0.75 m

Then,

The length of the carpet, AB = (22 – (2 × 0.75)) = (22 – (1.5)) = 20.5 m

The breadth of the carpet, AD = (15.5 – (2 × 0.75)) = (15.5 – (1.5)) = 14 m

∴Area of the carpet ABCD = (20.5 \times 14) \mathrm{m}^{2}=287 \mathrm{m}^{2}

Area of the Strip = (Area of PQRS – Area of ABCD)

= (341 – 287)

=54 \mathrm{m}^{2}

Now,

Area of 1 m of carpet = 1 × 0.82 = 0.82 \mathrm{m}^{2}

∴Length of the carpet whose area 287 \mathrm{m}^{2} = 287/0.82 = 350 m

Hence cost of 350 m long carpet = ₹ (60 × 350)

= ₹ 21000

Our top 5% students will be awarded a special scholarship to Lido.

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