# Precalculus/Trigonometry

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How can I write a polynomial equation for this problem and draw a labeled diagram?

A developer wants to build homes on a rectangular plot of land 4 kilometers long and 3 kilometers wide. In this part of the city, regulations require a greenbelt of uniform width along two adjacent sides. The greenbelt must be 10 times the area of the development. Find the width of the greenbelt.

• Precalculus/Trigonometry -

Let the greenbelt width be x. The developed area is (5-x)*(4-x). The greenbelt area is 5x + (4-x)x = 9x - x^2

The requirement is
9x - x^2 = 10 *(x^2 -9x +20)
11 x^2 -99 x +200 = 0
x^2 - 9x + 200/11 = 0

The labeled diagram is one rectangle nested inside a larger triangle with one pair of corners aligned, and a gap of x along the two perpendicular opposite sides

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