posted by Amanda on .
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.
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