Answer :
Answer:
To find the lengths of the sides of the garden, we'll use the given expressions for each side and the information about the perimeter.
Let's denote:
- \( x \) as the variable representing the length of one of the shorter sides of the trapezoid.
- \( y \) as the variable representing the length of the longer side of the trapezoid.
The perimeter of the trapezoid is the sum of all its sides:
\[ \text{Perimeter} = \text{Left Side} + \text{Right Side} + \text{Top} + \text{Bottom} \]
Given that the perimeter is 520 meters, we can write the equation as:
\[ 520 = 4(x-1) + 5x + 3(x+2) + (7x+5) \]
Now, let's solve for \( x \):
\[ 520 = 4x - 4 + 5x + 3x + 6 + 7x + 5 \]
\[ 520 = 19x + 7 \]
Subtracting 7 from both sides:
\[ 513 = 19x \]
Dividing both sides by 19:
\[ x = \frac{513}{19} \]
\[ x = 27 \]
Now that we have found \( x \), we can substitute it back into the expressions to find the lengths of each side:
- Left Side: \( 4(x-1) = 4(27-1) = 4(26) = 104 \) meters
- Right Side: \( 5x = 5(27) = 135 \) meters
- Top: \( 3(x+2) = 3(27+2) = 3(29) = 87 \) meters
- Bottom: \( 7x+5 = 7(27)+5 = 189+5 = 194 \) meters
So, the lengths of each side of the garden are:
- Left Side: 104 meters
- Right Side: 135 meters
- Top: 87 meters
- Bottom: 194 meters
Step-by-step explanation:
1. Set up the equation using the given expressions for each side and the perimeter of the trapezoid.
2. Simplify the equation by combining like terms.
3. Solve for the variable \( x \) by isolating it on one side of the equation.
4. Once \( x \) is found, substitute it back into each expression to find the lengths of each side.
5. Provide the final lengths of each side and label them accordingly.
