A rectangular plot is bounded at the back by a river. No fencing is needed along the river and there is to be an opening in front of about 24 meters. If the cost of fencing in front is $1500 per meter and the cost of fencing the sides is $1000 per meter, find the dimensions of the large plot which can be fenced for $300000.
x=56m
y=149.33m
To find the dimensions of the rectangular plot, we can start by assigning variables to the unknowns. Let's say the length of the plot is L and the width is W.
Given that there is no fencing needed along the back side (since it is bounded by a river), there are three sides that need to be fenced: the front side (which has an opening of 24 meters) and the two side boundaries.
The cost of fencing depends on the length of fencing required. The front side has a length of 24 meters and the two side boundaries have a length of L meters each.
Based on the given information, we can set up an equation for the cost of fencing:
Cost of fencing the front side + Cost of fencing the two side boundaries = Total cost of fencing
The cost of fencing the front side is $1500 per meter, multiplied by the length of the front side (24 meters), resulting in 1500 * 24 = $<<1500*24=36000>>36000.
The cost of fencing the two side boundaries is $1000 per meter, multiplied by the total length of the two side boundaries (2L meters), resulting in 1000 * 2L = 2000L.
The total cost of fencing is given as $300,000.
So, using the equation for the cost of fencing, we have:
36000 + 2000L = 300000
To find the value of L, we can solve this equation:
2000L = 300000 - 36000
2000L = 264000
L = 264000 / 2000
L = 132
Therefore, the length of the plot (L) is 132 meters.
To find the width (W) of the plot, we know that the front opening is 24 meters, and the total width will be the opening plus the two side boundaries, each of length L.
So, the width (W) can be calculated as:
W = 24 + 2L
W = 24 + 2 * 132
W = 24 + 264
W = 288
Therefore, the width of the plot (W) is 288 meters.
So, the dimensions of the large plot that can be fenced for $300,000 are 132 meters (length) by 288 meters (width).