Question

The number of tin sheets of side 20cm which can be formed from a tin sheet of side 1m is
[a] 5
[b] 25
[c] 50
[d] 100

Answer 1

Hint: Assume that the number of sheets which can be formed is x. Use the fact that the area of a square of side a is given by $A={{a}^{2}}$. Hence find the area of the tin sheets of side 20cm and the area of the tin sheet of side 1m. Use the fact that the total area of the smaller x tin sheets will be the area of the larger tin sheet of side 1m. Hence form an equation in x. Solve for x and hence find the number of sheets which can be formed. Verify your answer.
Complete step by step solution:

Let the number of tin sheets of side 20cm which can be formed using the tin sheet of side 20 m be x.
Now, we know that the area of a square of side a is given by $A={{a}^{2}}$
Hence the area of the square tin sheet of side 20 cm is $A={{20}^{2}}=400c{{m}^{2}}$
Also, we have
Length of side of the larger tin sheet = 1m = 100cm.
We know that the area of a square of side a is given by $A={{a}^{2}}$
Hence the area of the larger tin sheet of side 100m is ${{\left( 100 \right)}^{2}}=10000c{{m}^{2}}$
Now, we know that the total area of the smaller x tin sheets will be the area of the larger tin sheet of side 1m.
Hence, we have
$x\left( 400 \right)=10000$
Dividing both sides by 400, we get
$x=25$
Hence, the number of sheets which can be formed is 25.
Hence option [b] is correct.
Note: In the questions of mensuration students often make a mistake in taking the units of the terms involved. Units of the quantities should be kept the same e.g. metres and centimetres should not be compared. Many students forget to do that and end up with incorrect results.
Verification:
We can verify our solution by confirming that the area of 25 smaller sheets is equal to the area of the larger sheet.
Area of 25 square sheets of side 20 cm $=25\times {{\left( 20 \right)}^{2}}=10000c{{m}^{2}}$
Area of the square sheet of side 1m $=\left( 100cm \right)\left( 100cm \right)=10000c{{m}^{2}}$
Hence our answer is verified to be correct.
We can also verify from the diagram shown below

Hence our answer is verified to be correct.