the length breadth and height of a room are 8m 25cm 6m 75cm and 4m 50cm
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The length, breadth and height of a room are 8m 25cm, 6m 75cm and 4m 50cm, respectively. Determinethe longest rod which can measure the three dimensions of the room exactly.
Answer:
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 × 5 × 5 × 11
The same way prime factorization of 675 = 3 × 3 × 3 × 5 × 5
Prime factorization of 450 = 2 × 3 × 3 × 5 × 5
So the HCF of 825, 675 and 450 = 3 × 5 × 5 = 75
Therefore, the longest rod which can measure the dimensions of the room exactly is 75cm.Related Questions
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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 rod which can measure the three dimensions of the room exactly.
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 rod which can measure the three dimensions of the room exactly.
Byju's Answer Standard X Mathematics
Euclid's Division Lemma
The length, b... 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 rod which can measure the three dimensions of the room exactly.
Open in App Solution
We are given the length, breadth and height of a room as 8m 25cm, 6m 75cm and 4m 50cm, respectively. We need to determine the largest room which can measure the three dimensions of the room exactly.
We first convert each dimension in cm
Length of room = 8m 25cm = 825cm
Breadth of room = 6m 75cm = 675cm
Height of room = 4m 50cm = 450cm.
Therefore, the required longest rod = H.C.F. of 825, 675 and 450.
First we consider 675 and 450.
By applying Euclid’s division lemma
Therefore, H.C.F. of 675 and 450 = 225
Now, we consider 225 and 825.
By applying Euclid’s division lemma
Therefore, H.C.F. of 825, 675 and 450 = 75
Hence, the length of required longest rod is
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SIMILAR QUESTIONS
Q. The length, breadth and height of a room are 8m25cm,6m75cm and 4m50cm respectively. Find the length of the longest rod that can measure the three dimensions of the room exactly.Q. The length, breadth and height of a room are8 m 25 c m , 6 m 75 c m , and 4 m 50 c m
respectively. Find the length of the longest rod that can be fitted in the room exactly.
Q. The length, breadth and height of a room are12 m , 15 m and 18 m
respectively. Determine the longest tape which can measure all the three dimensions of the room exactly.
Q. 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 rod which can measure the three dimensions of the room exactly.Q.The length breadth height of room are 825cm 675cm and 450cm respectively find the longest tape which can measure the three dimensions of the room exactly
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Standard X Mathematics
The length, breadth and height of a room are 8m 25cm, 6 m 75 cm and 4 m 50 cm, respectively. Determine the longest rod which can measure the three dimensions of the room exactly.
The length, breadth and height of a room are 8m 25cm, 6 m 75 cm and 4 m 50 cm, respectively. Determine the longest rod which can measure the three dimensions of the room exactly.. Ans: Hint: First, we will convert the given dimensions into centimeter...
The length, breadth and height of a room are 8m 25cm, 6 m 75 cm and 4 m 50 cm, respectively. Determine the longest rod which can measure the three dimensions of the room exactly.
Last updated date: 12th Mar 2023
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Hint: First, we will convert the given dimensions into centimeters. Then we find the highest common factor, that is, H.C.F. of the given dimensions to find the longest rod which can measure the three dimensions of the room exactly.
Complete step-by-step answer:Given that the length, breadth and height of a room are 8m 25cm, 6 m 75 cm and 4 m 50 cm, respectively.
We know that 1 m=100 cm 1 m=100 cm .
First, we will convert the length of the room, that is, 8 m 25 cm in centimetres.
8×100+25=800+25 =825 cm
8×100+25=800+25=825 cm
Now we will convert the breadth of the room, that is, 6 m 75 cm in centimetres.
6×100+75=600+75 =675 cm
6×100+75=600+75=675 cm
We will now convert the length of the room, that is, 4 m 50 cm in centimetres.
4×100+50=400+50 =450 cm
4×100+50=400+50=450 cm
Prime factorizing the numbers 825 cm, 675 cm and 450 cm, we get
825=3×5×5×11 825=3×5×5×11 675=3×3×3×5×5 675=3×3×3×5×5 450=2×3×3×5×5 450=2×3×3×5×5
We will now find the common factors from the above prime factorization of 825, 765, and 450.
3×5×5 3×5×5
Multiplying the above numbers to find the H.C.F., we get
H.C.F.=75 H.C.F.=75
Thus, we now have that the highest common factor, i.e., H.C.F. of 825, 675 and 450 is 75.
Hence, the length of the longest tap is 75 cm, which can measure the three dimensions of the room exactly.
Note: In solving these types of questions, you should be familiar with the steps to find the highest common factor of the three numbers. The question is very simple to solve but students should be able to find the main point that the HCF of the length, breadth and height will be the length of the longest rod, which will measure the dimensions exactly. Then, calculate the H.C.F. without making any calculation mistakes.
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