SOLUTION: You are building a right-angled triangular flower garden along a stream as shown in the figure. The fencing of the left border costs $5 per foot, while the fencing of the lower bor

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Question 863972: You are building a right-angled triangular flower garden along a stream as shown in the figure. The fencing of the left border costs $5 per foot, while the fencing of the lower border costs $1 per foot. (No fencing is required along the river.) You want to spend $80 and enclose as much area as possible. What are the dimensions of your garden, and what area does it enclose? HINT [The area of a right-triangle is given by A = xy/2.]
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the left side and y be the bottom side.

Accounting for cost, 5x%2B1%2Ay=80.
Accounting for area, which you already did, A=%28xy%29%2F2.
Find A in terms of either variable x or y, and simplify.

y=80-5x from cost accounting.
A=x%2880-5x%29%2F2
A=%2880x-5x%5E2%29%2F2
A=-%285%2F2%29x%5E2%2B40x
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Factoring this will make x intercepts easy to find, and the maximum A will be the midpoint of the x intercept value.
A=x%2840-%285%2F2%29x%29
highlight_green%28x%2840-%285%2F2%29x%29=0%29
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x=0 OR (5/2)x=40, x=80/5=16
x=0 OR x=16
Maximum value of x is 8=x.
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According to the 80 dollar restriction, the maximum area occurs for highlight%28x=8%29 and highlight%28y=80-5%2A8=40%29.
AREA QUANTITY : 8%2A40%2F2=highlight%28160%29 square feet.