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Alik [6]
3 years ago
6

A landscape designer has to construct a rectangular flower bed with a perimeter of 100 feet and the maximum possible area. What

is the area of the flower bed
Mathematics
1 answer:
Alinara [238K]3 years ago
8 0

9514 1404 393

Answer:

   625 square feet

Step-by-step explanation:

The greatest area of a polygon with a given perimeter is that of a regular polygon. A regular rectangle is one that has all sides the same length -- a square. The side length of a square with 100 ft perimeter is 25 ft. The area of a square with such a side length is

  A = (25 ft)² = 625 ft²

The maximum possible area is 625 ft².

__

In the attached, x is the length of one side. The area versus side length is plotted. The maximum is seen to be 625 ft² for a side length of 25 ft.

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<h3><u>Solution:</u></h3>

Given, Micah places a mirror on the ground 24 feet from the base of a tree

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From the question, we can see there is a directly proportional relationship between heights and distances.

Proportional relationships are relationships between two variables where their ratios are equivalent.

\frac{\text { height of micah eyes above ground }}{\text { distance of micah from mirror }}=\frac{\text { height of tree above the ground }}{\text { distance of tree from mirror }}

\begin{array}{l}{\frac{6 \text { feet }}{9 \text { feet }}=\frac{n \text { feet }}{24 \text { feet }}} \\\\ {\frac{6}{9}=\frac{n}{24}} \\\\ {\text { n }=\frac{1}{3} \times 24} \\\\ {\text { n }=8}\end{array}

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