Question

A rectangular courtyard 1.12 m long and 0.84 m wide is to be paved exactly with square tiles , all of same size.The largest size of the tile which could be used for the purpose is (n × 4)cm.Find the value of n.​

Answer 1

The largest size of the tile which could be used for the purpose is $(7\times 4)\ cm$. So, the value of 'n' is 7.

Step-by-step explanation:

Given:

Length of the rectangular courtyard is, $L=1.12\ m=1.12\times 100=112\ cm$

Width of the rectangular courtyard is, $W=0.84\ m=0.84\times 100 = 84\ cm$

Now, to find the largest size of the square tile to be paved, we need to find the common factors of the length and width.

The factors of 112 = $2\times 2\times 2\times 2\times 7$

The factors of 84 = $2\times 2\times 3\times 7$

Therefore, the common factors of both 112 and 84 are $2\times 2\times 7=(7\times 4)cm$

Therefore, on comparing with the given form $(n\times 4)cm$ with $(7\times 4)cm$, we get the value of 'n' as 7.