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 $$l_1.$$
$$\begin{array}{rl}& 900=l_1\times 30\\ & \therefore l_1={\displaystyle \frac{900}{30}}=30cm\end{array}$$
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 $$l_2$$.
$$\begin{array}{rl}& 1350=l_2\times 45\\ & \therefore l_2={\displaystyle \frac{1350}{45}}=30cm\end{array}$$
$$\therefore$$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.