Question

7. A farmer is fencing in part of his cattle's

grazing land. He would like the shape to be a
rectangle, but he will use the nearby river as
one side of the pen. He knows that he would
like the length of the pen to be 4w - 2 meters
and the width to be w meters. If the farmer has
550 square meters of land to enclose and the
river is parallel to the length of the pen,
answer the questions that follow.
a) Draw a picture to represent the situation
b) What is the length and width of the pen in
meters?
c) How many total meters of fencing will the
farmer need to build the pen?

Answer 1

To enclose the grazing land with a river as one side, the pen should have a length of 56 meters and a width of 14 meters. The farmer will need 10w + 52 meters of fencing to enclose the pen.

Step-by-step explanation:

To represent the situation, draw a rectangle and label one side as the river. Let the width of the pen be w meters and the length be 4w - 2 meters.

To find the values of w and the length, use the fact that the area of the rectangle is 550 square meters. Multiply the width and length and set it equal to 550. Solve this equation to find w = 14 and the length = 56 meters.

To find the total meters of fencing needed, add up the lengths of all the sides of the pen. Since the river is one side, the farmer needs to find the perimeter of the rectangle by adding the length and width (2w) twice. The total meters of fencing needed is 2(4w - 2) + 2w + 56 = 10w + 52 meters.

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