Jane is fencing in her backyard. The yard is a rectangular area where one side is the back of her house. The fence will go around only the other 3 sides. The side opposite the house is the same length as the house, which is 25 feet. Jane will use 120 feet of fencing.
Which equation can Jane use to decide how long each of the other two sides of her fence can be?
A. [tex]$x+25=120$[/tex]
B. [tex]$x+x+25=120$[/tex]
Answer (1)
Define x as the length of the two equal sides of the fence.
Express the total length of the fence as x + x + 25 .
Set the total length equal to the amount of fencing available: x + x + 25 = 120 .
The equation to find the side length is x + x + 25 = 120 .
Explanation
Understanding the Problem Let's analyze the problem. Jane is fencing her backyard, which is rectangular. One side of the rectangle is the back of her house, and the fence covers the other three sides. The side opposite the house is 25 feet long, and the total fencing used is 120 feet. We need to find the equation that represents this situation.
Setting up the Equation Let x be the length of each of the two equal sides of the fence that are perpendicular to the house. The total length of the fence is the sum of the lengths of these three sides: x + x + 25 . Since Jane uses 120 feet of fencing, we can set up the equation: x + x + 25 = 120 .
Final Equation Therefore, the equation Jane can use to decide how long each of the other two sides of her fence can be is x + x + 25 = 120 .
Examples
Imagine you're designing a dog pen where one side is already formed by your house. Knowing the total amount of fencing you have and the length of the house-side, you can use this equation to determine the dimensions of the pen, ensuring your furry friend has enough space to play safely. This type of problem is also useful in gardening, where you might want to enclose a rectangular garden bed against a wall or fence, optimizing the use of available materials and space.
