Question

Which carpet is bigger: one measuring 16m in length and 12.5m in breadth or another measuring 15m in length and 13.8m in breadth.

Answer 1

Hint:
First, We will calculate the area of both the carpets individually, since the carpets are usually rectangular, we will use the formula of area of a rectangle to find their respective areas, After that, we will compare the two calculated areas and the one which is found to be greater would have a bigger carpet associated with it. Hence, that would be the bigger carpet and the final answer too.

Complete step by step solution:
We know that area of a rectangle whose length (L) and breadth (B) is known is given by,
 ${A_{rectangle}} = L \times B$ . … (1)

Carpet 1 has a length of \[L = 16\] and breadth of \[B = 12.5\]
Hence, put \[L = 16\] and \[B = 12.5\] in (1), we get the area of the first carpet as
 $ \Rightarrow {A_{carpet\,1}} = 16 \times 12.5$
On Simplification we get,
 $ \Rightarrow {A_{carpet\,1}} = 200\,\,{m^2}$ … (1)
Hence, the area of carpet\,1 is $200{m^2}$

Carpet 2 has a length of \[L = 15\] and breadth of \[B = 13.8\]
Hence, put \[L = 15\] and \[B = 13.8\] in (1), we get the area of the first carpet as
$ \Rightarrow {A_{carpet\,2}} = 15 \times 13.8$
On simplification we get,
$ \Rightarrow {A_{carpet\,2}} = 207\,\,{m^2}$ … (2)
Hence, the area of carpet 2 is $207\,\,{m^2}$

Hence, comparing (1) and (2), we get
 $ \Rightarrow {A_{carpet\,2}} > {A_{carpet\,1}}$

Therefore, carpet 2 is bigger than the carpet 1.

Note:
These types of questions may seem easy but we should always remember to check that all the measurements given are in a common unit, if not then convert all of them in a common unit. Luckily in our question, there was no need for unit conversion, otherwise unit conversion should be our FIRST and the most important step.