7.
The length, breadth and height of a room are 8.25 m, 6.75 m and 4.50
respectively. Determine the longest tape which can measure the three dimensions
of the room exactly.
Answers
Answer:
75cm
Step-by-step explanation:
Length, breadth and height of a room are 8 m 25 cm, 6 m 75 cm and 4 m 50 cm, respectively.
Length = 825 cm
Breadth = 675 cm
Height = 450 cm
HCF of 825, 675, 450
825 = 5 x 5 x 3 x 11
675 = 5 x 5 x 3 x 3 x 3
450 = 2 x 3 x 3 x 5 x 5
HCF = 5 x 5 x 3 = 75cm
∴ , the length of the longest rod which can measure the three dimensions of the room exactly is 75 cm
♡Given:-
Dimensions of the room-
⚫ Length = 8m 25cm
⚫ Breadth = 6m 75cm
⚫ Height = 4m 50cm
♡To find:-
⚫ Length of tape which can measure all the dimensions exactly.
So, we will have to find the Highest common factor of the dimensions
♡Solution:-
➣ 8m 25cm = 825 cm
➣ 6m 75cm = 675 cm
➣ 4m 50cm = 450 cm
Prime factorization of 825, 675 and 450:-
⤍ 825 = 3×5×5×11
⤍ 675 = 3×3×3×5×5
⤍ 450 = 2×3×3×5×5
Common factors = 3×5×5
- H.C.F = 75
∴ the length of the longest tape which can measure the three dimensions of the room exactly is 75 cm.