Question

If the breadth of rectangle 1 and rectangle 2 is 30 cm and 45 cm respectively, the area of rectangle 1 is \[900c{{m}^{2}}\] and area of rectangle 2 is \[1350c{{m}^{2}}\], then compare the lengths of the rectangle.
A. both are same
B. length of rectangle 1 is greater than rectangle 2
C. length of rectangle 2 is greater than rectangle 1
D. none of these

Answer 1

Hint: Use the formula of the area of the rectangle. Find the length of rectangle 1 and rectangle 2 separately with the given data. Compare both the lengths obtained.

Complete Step-by-step answer:
First, let represent the given rectangles, as shown below:

Let us find the length of rectangle 1.
Given to us is the breadth of rectangle 1 as 30 cm. Let us consider the breadth as \[{{b}_{1}}.\]
\[\therefore {{b}_{1}}=30cm\]
Let us assume the length of rectangle 1 as \[{{l}_{1}}.\]
We have been given the area of rectangle 1 as \[900c{{m}^{2}}\], i.e. let us take it as \[{{A}_{1}}.\]
\[\therefore {{A}_{1}}=900c{{m}^{2}}.\]
We know that area of rectangle \[=length\times breadth\]
Area of rectangle 1 \[=length\times breadth\]
\[{{A}_{1}}={{l}_{1}}{{b}_{1}}\]
We know \[{{A}_{1}}\] and \[{{b}_{1}}.\]Find \[{{l}_{1}}.\]
\[\begin{align}
& 900={{l}_{1}}\times 30 \\
& \therefore {{l}_{1}}=\dfrac{900}{30}=30cm \\
\end{align}\]
Thus the length of rectangle 1 \[={{l}_{1}}=30cm.......(1)\]
Now let us find the length, \[{{l}_{2}}\] of rectangle 2.
The breadth \[{{b}_{2}}\]of rectangle 2 is given as 45 cm.
The area of rectangle 2, \[{{A}_{2}}\], is given as \[1350c{{m}^{2}}\].
Thus area of rectangle \[=length\times breadth\]
\[{{A}_{2}}={{l}_{2}}{{b}_{2}}\]
We know \[{{A}_{2}}=1350c{{m}^{2}}\], \[{{b}_{2}}=45cm\]. Find \[{{l}_{2}}\].
\[\begin{align}
& 1350={{l}_{2}}\times 45 \\
& \therefore {{l}_{2}}=\dfrac{1350}{45}=30cm \\
\end{align}\]
\[\therefore \]Length of rectangle 2 \[={{l}_{2}}=30cm.......(2)\]
Now let us compare the length of both rectangle 1 and 2.
\[{{l}_{1}}=30cm\] and \[{{l}_{2}}=30cm\]
\[\therefore {{l}_{1}}={{l}_{2}}=30cm\].
Hence the length of both rectangles 1 and 2 are the same.
Option A is the correct answer.

Note: The area of the rectangle is a basic formula, so you should remember the formula. This question was a basic application of the area of rectangles. After finding the lengths, don’t forget to compare the lengths of rectangle 1 and rectangle 2.