To find the length of the rectangular ground given the ratio of length to breadth and the measurement of the breadth, follow these steps:
1. Interpret the given ratio: The ratio of the length to the breadth of the rectangular ground is given as 4:3. This means that for every 4 units of length, there are 3 units of breadth.
2. Identify the known value: We are given that the breadth of the ground is 75 meters.
3. Set up the proportion: According to the ratio [tex]\(4:3\)[/tex], let:
- [tex]\(L\)[/tex] represent the length,
- [tex]\(B\)[/tex] represent the breadth.
The ratio can be written as:
[tex]\[
\frac{L}{B} = \frac{4}{3}
\][/tex]
4. Substitute the known value into the equation: Since the breadth [tex]\(B = 75\)[/tex] meters, substitute this value into the proportional equation:
[tex]\[
\frac{L}{75} = \frac{4}{3}
\][/tex]
5. Solve for the length [tex]\(L\)[/tex]: To find [tex]\(L\)[/tex], cross-multiply the proportion:
[tex]\[
L = \left( \frac{4}{3} \right) \times 75
\][/tex]
6. Calculate the result: Perform the multiplication:
[tex]\[
L = \frac{4 \times 75}{3}
\][/tex]
[tex]\[
L = \frac{300}{3}
\][/tex]
[tex]\[
L = 100
\][/tex]
Therefore, the length of the ground is 100 meters.
