a house is 40 feet wide and 60 feet long a lady wants to use 260 feet of fencing to fence an area behind her house. the back of the backyard is 60x+2x and one side is 200-4x divided by 2. the back yard is a rectangle shape
so, add up the sides to make 260.
That will give you x, and thus the dimensions of the yard.
To find the dimensions of the backyard, we can set up an equation using the given information. Let's break it down step by step:
1. Identify the known information:
- The width of the house is 40 feet.
- The length of the house is 60 feet.
- The total amount of fencing available is 260 feet.
2. Define the variables:
- Let's use the variable "x" to represent the length of one side of the backyard.
3. Determine the dimensions of the backyard:
- The back of the backyard is described as having a length of 60x + 2x. Since the house is connected to one side of the backyard, this length is equal to the width of the house. So we have 60x + 2x = 40.
- Simplifying the equation: 62x = 40.
- Dividing both sides by 62: x = 40 / 62.
- Calculating the value of x: x ≈ 0.645 feet.
4. Calculate the sides of the backyard:
- The length of the backyard is 60x + 2x = 60(0.645) + 2(0.645) = 38.7 + 1.29 ≈ 39.99 feet (approximately 40 feet).
- The width of the backyard is 200 - 4x divided by 2: (200 - 4(0.645)) / 2 = (200 - 2.58) / 2 ≈ 98.21 / 2 ≈ 49.11 feet (approximately 49 feet).
Therefore, the dimensions of the backyard are approximately 40 feet by 49 feet.