Question : The length, breadth, and height of a room are 6 m, 4 m 80 cm, and 3 m 60 cm respectively. Find the longest tape that can measure the dimensions of the room exactly.
Option 1: 1 m 40 cm
Option 2: 1 m 20 cm
Option 3: 1 m 80 cm
Option 4: 1 m 50 cm
Correct Answer: 1 m 20 cm
Solution :
According to the question
Length = 6 m = 6 ×100 cm = 600 cm
Breadth = 4.80 m = 4.80 × 100 cm = 480 cm
Height = 3.60 m = 3.60 × 100 cm = 360 cm
Find the prime factors of the numbers.
Length = 600 = 2 × 2 × 2 × 3 × 5 × 5
Breadth = 480 = 2 × 2 × 2 × 2 × 2 × 3 × 5
Height = 360 = 2 × 2 × 2 × 3 × 3 × 5
Longest tape = Highest common factor (HCF) of the room's height, length, and breadth.
⇒ HCF = 2 × 2 × 2 × 3 × 5 = 120 cm = 1 m 20 cm
Hence, the correct answer is 1 m 20 cm.
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