Question

the length breadth and height of a room are are 8 metre 25 CM ,6 metre 75 cm and 4 metre 50 cm respectively. determine the longest tape which can measure the dimension of the room exactly​

Answer 1

Given :

• Length of the room = 8 m 25 cm
• Breadth of the room = 6 m 75 cm
• Height of the room = 4 m 50 cm

To Find :

The longest tape which can measure the dimension of the room.

Solution :

Analysis :

Here we will first be converting the length, breadth and height to centimeter (cm). After that we have to take out the Highest Common Factor (H.C.F) of length, breadth and height of the room. Then we have to check the numbers which are common is all the three. After taking out the common numbers we will multiply which will be our H.C.F. If all the three length, breadth and height is divisible by the H.C.F then that number will become the longest tape to be measured.

Explanation :

The Dimensions in cm :

1 m = 100 cm

• Length = 8 m 25 cm = 800 + 25 = 825 cm
• Breadth = 6 m 75 cm = 600 + 75 = 675 cm
• Height = 4 m 50 cm = 400 + 50 = 450 cm

Now we know that,

For any rod to be capable of measuring a side, the length of the side must be a multiple of the length of the rod.

Longest tape = H.C.F of 825, 675, 450

So, first let's take out the H.C.F of 825, 675, 450 by prime factorisation.

• 825 = 3 × 5² × 11

• 675 = 3³ × 5³

• 450 = 2 × 3² × 5²

From the above we can see that 3 and 5² are common in all the three.

So,

H.C.F = 3 × 5² = 3 × 5 × 5 = 75

∴ H.C.F of 825, 675, 450 = 75.

75 is divisible by all the three 825, 675 and 450.

∴ Longest Tape = 75 cm.

The longest tape which can measure the dimension of the room is 75 cm.