The length, breadth, hight of a room are 720cm, 560cm, and 4cm respectively. find the length of the longest tape which can measure the three dimensions of the room exactly.
Answers
Answer: Given the length of room = 825cm.
Breadth of the room = 675cm.
Height of the room = 450cm.
We need to find the longest tape that is capable of measuring the sides.
So to find the length of tape, we need the length of tape which is a factor of 825, 675 and 450cm.
So if we need to find the tape of the highest possible length that we need to find HCF of 825, 675 and 450.
By prime factorization, we can find the HCF. Prime factorization is finding which prime number multiplies together to make the original number.
A prime number is a number greater than 1 that cannot be made into a whole number. For a prime number the only factors are 1 and itself.
Now let us find the prime factorization of 825, 675 and 450.
825=3×5×5×11=3×52×11
675=3×3×3×5×5=33×52
450=2×3×5×3×5=2×32×52
From the above, we can say that (3×52)
is common for 825, 675 and 450.
∴
HCF (825, 675, 450) = 3×5×5=75
.
Hence, we got HCF = 75.
∴
The longest tape which can measure the three dimensions of a room exactly will be 75cm long.
∴
Option (d) is the correct answer.
Note: We can also find HCF using different methods.
∴825=3×5×5×11
675=3×3×3×5×5
450=2×3×3×5×5
Step-by-step explanation: