Question

Lenth 8m 25 cm breath 6m 75cm and height 4m 50cm respectively. Determine the longest rod which can measure the three dimensions of the room exactly.

Answer 1

Given :

• Lenth 8m 25 cm breath 6m 75cm and height 4m 50cm respectively

To find :

• Determine the longest rod which can measure the three dimensions of the room exactly.

Solution:

The dimensions of room are

Length = 8m 25cm = 825cm

Breadth = 6m 75cm = 675cm

Height = 4m 50cm = 450cm

So the longest rod = HCF of 825, 675 and 450

We know that the prime factorization of 825

= 3 x 5 x 5 x 11

The same way prime factorization of 675

= 3 x 3 x 3 x 5 x 5

Prime factorization of 450

= 2 x 3 x 3 x 5 x 5

So the HCF 825, 675 and 450

= 3 x 5 x 5

= 75

Therefore, the longest rod which can measure the dimensions of the room exactly is 75cm.

Answer 2

Answer:

⭐ Given ⭐

$\mapsto$ The length, breadth and height of a room is 8m 25cm, 6m 75 cm and 4m 50 cm respectively.

⭐ To Find ⭐

$\mapsto$ What is the longest rod which can measure the three dimensions of the room exactly.

⭐ Solution ⭐

➕ Length of the room = 8m 25cm = 825 cm

➕ Breadth of the room = 6m 75cm = 675 cm

➕ Height of the room = 4m 50cm = 450 cm

$\green\bigstar$ Prime factorization of 825, 625 and 450 are as follows :-

✴️ 825 = 3×5×5×11

✴️ 675 = 3×3×5×5

✴️ 450 = 2×3×3×5×5

✳️ Common factors = 3×5×5

✳️ H.C.F = 75

Hence, H.C.F of 825, 625 and 450 is 75.

$\therefore$ The longest rod which can measure the three dimensions of the room exactly is 75.

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