Answer:
Explanation:
Let's break down the problem step by step.
1. We are given that the area of a square is 4 sq. m more than 64 sq. m. So, the area of the square is \(64 \, \text{sq. m} + 4 \, \text{sq. m} = 68 \, \text{sq. m}\).
2. We also know that the area of a square is simply the side length squared. So, if \(s\) is the side length of the square, then \(s^2 = 68 \, \text{sq. m}\).
3. Next, we are given that the length of a rectangle is three-fourths (3/4) of its breadth. Let's call the breadth of the rectangle \(b\) meters. So, the length of the rectangle would be \(\frac{3}{4}b\) meters.
4. The area of the rectangle is given by \(A_{\text{rectangle}} = \text{Length} \times \text{Breadth}\). Substituting the values, we have \(A_{\text{rectangle}} = \left(\frac{3}{4}b\right) \times b = \frac{3}{4}b^2\).
5. We know that the area of the square is equal to the area of the rectangle. So, we can set up an equation:
\[s^2 = \frac{3}{4}b^2\]
6. Now, we can solve this equation for \(b\) (breadth):
\[b^2 = \frac{4}{3}s^2\]
\[b = \sqrt{\frac{4}{3}s^2}\]
7. Since \(s\) is the side length of the square (which we already found to be \(s = \sqrt{68}\)), we can substitute this value into the equation to find \(b\):
\[b = \sqrt{\frac{4}{3} \cdot 68}\]
Now, you can calculate the value of \(b\), which will be the breadth of the rectangle. Once you have the breadth, you can find the length of the rectangle by using the fact that it's three-fourths of the breadth.