Question

the length breadth and height of a room are 8 m 25 cm,6 m 75 cm and 4 m 50 cm,respectively.Determine the longest tape which can measure the three dimensions o the room.

Answer 1

HEY DEAR ... ✌️


_______________________


_______________________


Length of the room = 8.25 m or 825 cm

Breadth of the room = 6.75 m = 675 cm

Height of the room = 4.50 m = 450 cm

We have to find the longest rod that can measure the three dimensions of the room exactly. For this, we have to find the Highest Common Factor of 825, 675 and 450.

Prime factorization of 825 = 3×5×5×11

Prime factorization of 675 = 3×3×3×5×5

Prime factorization = 450 = 2×3×3×5×5

Common factors = 3×5×5

H.C.F. = 75

Hence, H.C.F. of 825, 675 and 450 is 75

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


_________________________


HOPE , IT HELPS ... ✌️

Answer 2

Step-by-step explanation:

Initially,The given values are 825cm, 675cm, 450cm.

Basically we need to find the length{in cm} of rod which is a factor of 825,675 and 450.

By using Prime Factorization:-

825=3x5²x11

675=3²x5²

450=2x3²x5²

From the above factorization,We got H.C.F⇒3x5²=75.

∴The Longest length rod Which measures the 3 dimensions of the room exactly will surely be "75cm Long".