SOLUTION: The rectangular plot of land shown in the figure is to be fenced along three sides using 35 feet of fencing. No fencing is to be placed along the river's edge. The area of the plot
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Question 1180439: The rectangular plot of land shown in the figure is to be fenced along three sides using 35 feet of fencing. No fencing is to be placed along the river's edge. The area of the plot is 150 square feet. What are its dimensions?
a. 15 ft by 10 ft or 20 ft by 7.5 ft
b. 30 ft by 5 ft or 20 ft by 7.5 ft
c. 15 ft by 10 ft
d. 20 ft by 7.5 ft Found 2 solutions by josgarithmetic, ikleyn:Answer by josgarithmetic(39617) (Show Source):
You can put this solution on YOUR website! Showing the figure would be a good idea, which you did not do.
The fence for sides x, x, and y: , and for the given area, .
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If use general solution for quadratic equation, the solution which makes sense is .
This problem has 2 (two, TWO) solutions, listed under the answer option (a).
Namely, one solution is 15 ft parallel to the river and 10 ft perpendicular to it.
The other solution is 20 ft parallel to the river and 7.5 ft perpendicular to it.
All other answer options DO NOT WORK: they are not the full solutions to the problem.
Notice, that @josgarithmetic lost one of the solutions in his post.
The problem can be solved by using the quadratic equation, as @josgarithmetic tried to do in his post,
but failed to complete it accurately.
The problem ALSO can be solved WITHOUT USING EQUATION/EQUATIONS by inspection, simply checking
all presented options directly by crude force.
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