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Playing with numbers | Playing with numbers Exercise 2.8

Question 5

A rectangular courtyard is 20m 16cm long and 15m 60cm broad. It is to be paved with square stones ofthe same size. Find the least possible number of such stones.

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The dimensions of courtyard are

Length = 20m 16cm = 2016cm

Breadth = 15m 60cm = 1560cm

Least possible side of square stones used = HCF of 2016 and 1560

We know that the prime factorization of 2016 = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 7

1560 = 2 × 2 × 2 × 3 × 5 × 13

So HCF of 2016 and 1560 = 2 × 2 × 2 × 3 = 24

Hence, the least possible side of square stones used is 24cm.

We know that

No. of square stones which is used to pave the rectangular courtyard = Area of courtyard/ Area of stone By substituting the values

No. of square stones which is used to pave the rectangular courtyard = (2016 × 1560)/ (24)2 = 5460 Therefore, the least possible number of such stones is 5460.

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

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Question 5

A rectangular courtyard is 20m 16cm long and 15m 60cm broad. It is to be paved with square stones ofthe same size. Find the least possible number of such stones.

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

The dimensions of courtyard are

Length = 20m 16cm = 2016cm

Breadth = 15m 60cm = 1560cm

Least possible side of square stones used = HCF of 2016 and 1560

We know that the prime factorization of 2016 = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 7

1560 = 2 × 2 × 2 × 3 × 5 × 13

So HCF of 2016 and 1560 = 2 × 2 × 2 × 3 = 24

Hence, the least possible side of square stones used is 24cm.

We know that

No. of square stones which is used to pave the rectangular courtyard = Area of courtyard/ Area of stone By substituting the values

No. of square stones which is used to pave the rectangular courtyard = (2016 × 1560)/ (24)2 = 5460 Therefore, the least possible number of such stones is 5460.

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

subject-cta
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