explanation ;
Let's denote the length of the rectangle as "l" and the width as "w".
From the problem statement, we know that the perimeter of the fence is 28 feet, so:
2l + 2w = 28
Simplifying this equation, we get:
l + w = 14
We also know that two opposite sides cost $10 per foot, and the other two sides cost $12 per foot. This means that the total cost of the fence is:
10(2l) + 12(2w) = 20l + 24w
We are told that the total cost of the fence is $148, so:
20l + 24w = 148
Now we have two equations with two unknowns, which we can solve simultaneously.
We can solve for one variable in terms of the other, and substitute that expression into the other equation. For example, we can solve the first equation for l in terms of w:
l = 14 - w
Substituting this into the second equation, we get:
20(14 - w) + 24w = 148
Simplifying this equation, we get:
280 - 20w + 24w = 148
4w = 132
w = 33
Now that we know the width is 33 feet, we can use the first equation to solve for the length:
l + w = 14
l + 33 = 14
l = -19
This answer doesn't make sense, since the length of the fence can't be negative.
We made an error somewhere, so let's go back and check our work.
We can start by checking our equation for the cost of the fence:
10(2l) + 12(2w) = 20l + 24w
This equation is correct, but we made a mistake when we substituted l = 14 - w into it.
We should have substituted l = 14 - w into the first equation, and solved for w:
l + w = 14
14 - w + w = 14
w = 7
Now we can use this value of w to solve for l:
l + w = 14
l + 7 = 14
l = 7
Therefore, the dimensions of the fence are 7 feet by 7 + 7 + 6 + 6 = 26 feet.
The answer is not
Hopefully this helps ;)