Question

. The length, breadth and height of a room are 825 cm, 675 cm and 450 cm respectively. Find the

longest tape which can measure the three dimensions of the room exactly.​

Answer 1

Answer:

Step-by-step explanation:

Given :-

Length = 8 m 50 cm = 850 cm  

Breadth = 6 m 75 cm = 675 cm  

Height = 4 m 50 cm = 450 cm

To Find :-

Length of the longest rod.

Formula to be used :-

HCF of given dimensions

Solution :-

we have to find the HCF of 825, 675 and 450 .

825 = 5 × 5 × 3 × 11

675 = 5 × 5 × 3 × 3 × 3

450 = 2 × 3 × 3 × 5 × 5

HCF = 5 × 5 × 3

HCF = 75 cm

Hence, the length of the longest rod which can measure the three dimensions of the room exactly is 75 cm.

Answer 2

Longest tape which can measure the three dimensions of the room exactly= HCF of 825 cm, 675 cm and 450 cm

825=3×5×5×11

675=3×3×3×5×5

450=2×3×3×5×5

HCF of 825,675 and 450=3×5×5= 75

Longest tape which can measure the three dimensions of the room exactly=75 cm