Question

the length and the breadth of a rectangular field are 55m and 45m respectively. determine the length in metres of the largest rod which can measure the length and breadth of the field exactly
(CH1 REAL NUMBERS CLASS X)

Answer 1

Answer:

71 m

Step-by-step explanation:

55*55 + 45*45

= 3025 + 2025

= √5050

~= 71 m

Answer 2

Answer:

Required length of the rod is 5 m.

Step-by-step explanation:

Given that the length and breadth of a rectangular field is 55 m and 45 m respectively.

The length of the longest rod that can measure both the length and breadth of the field exactly will be the highest common factor (HCF) of the length and breadth.

Therefore, factorise 55 as follows:

$55=5×11$

Now, factorise 45 as follows:

$45=3 \times 3×5$

We know that HCF is the highest common factor.

Since the common factor between the numbers 55 and 45 is $5$

So,HCF of 55 and 45 is 5.

Hence, the length of the longest rod which can measure the length and breadth of the field exactly, is 5 m.

Some important formulas about rectangle,

If length and breadth of a rectangle are l and b respectively then

1.Perimeter$= 2 \times (l + b) \: unit$

2.Area$= (l \times b) \: square \: unit$

3.Length of the diagonal $= \sqrt{ {l}^{2} + {b}^{2} } \: unit$