Answer:
Step-by-step explanation:To find the dimensions of the rectangle farmland with an area of 7200m² and a perimeter of 360m, we need to use the formulas for area and perimeter of a rectangle.
1. Let the length of the rectangle be \( L \) and the width be \( W \).
2. The formula for the area of a rectangle is \( \text{Area} = \text{Length} \times \text{Width} \).
3. Given that the area is 7200m², we have \( L \times W = 7200 \).
4. The formula for the perimeter of a rectangle is \( \text{Perimeter} = 2(\text{Length} + \text{Width}) \).
5. Given that the perimeter is 360m, we have \( 2(L + W) = 360 \).
Now, we have two equations:
- Equation 1: \( L \times W = 7200 \)
- Equation 2: \( 2(L + W) = 360 \)
We can solve these equations simultaneously to find the dimensions of the farmland. One way to approach this is by substitution or elimination.
Let's solve the equations:
From Equation 1, we can express \( L \) in terms of \( W \): \( L = \frac{7200}{W} \).
Substitute this expression for \( L \) into Equation 2:
\( 2\left(\frac{7200}{W} + W\right) = 360 \).
Simplify:
\( \frac{14400}{W} + 2W = 360 \).
Multiplying by \( W \) to get rid of the fraction:
\( 14400 + 2W^2 = 360W \).
Rearrange the equation:
\( 2W^2 - 360W + 14400 = 0 \).
This is a quadratic equation that can be solved using the quadratic formula or factoring.
Once you find the values of \( W \) (width) and \( L \) (length), you will have the dimensions of the rectangle farmland.
