A fence encloses a rectangular field. The field is 4 meters longer that it is wide. The total length of the fence is 144 meters. What is the area in square meters of the enclosed field?
Choices
1,192
1296
1292
1440
I have tried dividing but getting know where. :( Help with steps please?
What am I doing wrong? it throws me off when it says, 4 meters longer than it is wide.
144 = 2L + 2 w
so
L + w = 72
L = w + 4
so
w + 4 + w = 72
2 w = 68
w = 34
then L = 38
A = L * w = 38 * 34 = 1292
Thank you!! Damon. I really appreciate you guys being here. I am writing this in my notes. Thank you again.
To solve this problem, let's break it down step by step:
Step 1: Define the variables.
Let's say the width of the field is 'w' meters. Since the length is 4 meters longer than the width, the length of the field would be 'w + 4' meters.
Step 2: Write the equation for the perimeter.
The perimeter of a rectangle is calculated by adding all four sides. In this case, we have two sides of width 'w' and two sides of length 'w + 4'. The total perimeter is given as 144 meters, so we can write the equation as follows:
2w + 2(w + 4) = 144
Step 3: Simplify the equation.
To simplify this equation, distribute the 2 to both 'w' and 'w + 4':
2w + 2w + 8 = 144
Combine like terms:
4w + 8 = 144
Step 4: Isolate the variable 'w'.
To isolate 'w', subtract 8 from both sides of the equation:
4w = 136
Then, divide both sides by 4:
w = 34
Step 5: Calculate the length of the field.
Since the length is 4 meters longer than the width, we substitute the value of 'w' into the equation:
Length = w + 4 = 34 + 4 = 38 meters
Step 6: Calculate the area of the field.
The area of a rectangle is calculated by multiplying the length and width. In this case, the width is 34 meters and the length is 38 meters:
Area = length × width = 34 × 38
Calculating this:
Area = 1292 square meters
Therefore, the area of the enclosed field is 1292 square meters, which matches option 3.