the length breadth and height of a room are 825cm,675cm, and 450cm . find the longest tape which can measure the three dimensions of the room exactly.
Answers
To find the length of the longest tape which can measure the three dimensions of the room, we need to find the H.C.F of length, breadth and height of the room respectively.
Length of the room = 825 cm
Breadth of the room = 675 cm
Height of the room = 450 cm
Let us factorize all three given dimensions.
- 825 = 3 × 5 × 5 × 11
- 675 = 3 × 3 × 3 × 5 × 5
- 450 = 2 × 3 × 3 × 5 × 5
Hence, 3, 5 and 5 are the common prime factors here.
So, H.C.F =3 × 5 × 5
H.C.F = 75 cm
Therefore, we need 75 cm the longest tape to measure the three dimensions of the room.
Length of the room = 825 cm
Breadth of the room = 675 cm
Height of the room = 450 cm
Let us factorize all three given dimensions.
825 = 3 × 5 × 5 × 11
675 = 3 × 3 × 3 × 5 × 5
450 = 2 × 3 × 3 × 5 × 5
Hence, 3, 5 and 5 are the common prime factors here.
So, H.C.F =3 × 5 × 5
H.C.F = 75 cm
Therefore, we need 75 cm the longest tape to measure the three dimensions of the room.